Systems and methods related to bond valuation

Description

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application No. 61/864,817, filed Aug. 12, 2013, entitled “Systems and Method Related to Bond Valuation” and to U.S. Provisional Patent Application No. 61/936,096, filed Feb. 5, 2014, entitled “Systems and Methods Related to Bond Valuation.” The entire contents of each of the above-referenced applications are incorporated herein by reference.

INTRODUCTION

Effective valuation of fixed income instruments, such as corporate bonds, is an essential input to various activities within capital markets, including bond trading, risk management and financial reporting. Unlike equity instruments, whose issuance typically is concentrated in one issue per issuing entity (or potentially a small number of stock “classes”), fixed income issuers may have tens, hundreds, or even thousands of issues outstanding. Each of these instruments might have different features and may have differing levels of liquidity. Consequently, even with the accessibility of trade data for certain corporate bonds through the FINRA TRACE system, trade frequency is inconstant and analysis is required to ascertain bond valuation at any moment in time.

To date, this analysis has generally been a labor-intensive process, such that valuations are generally produced with limited frequency, such as once or twice per day. However, new data made available through TRACE in November 2008, as well as the increased trading of fixed income exchange traded funds (“ETFs”) have made possible an algorithmic valuation process for corporate bonds. Contained within TRACE data is an indicator that identifies whether the reporting entity (the dealer) bought the bond from a client (a “dealer buy”), sold the bond to a client (a “dealer sell”) or traded the bond with another dealer (an “interdealer transaction”). Dealer buys thus imply the “bid” side of the market, dealer sells imply the offer side, and the interdealer transactions imply the “mid” market. The research leading to certain embodiments has shown that the distance between a bid and ask differs according to the size of the transaction and to the bond itself.

Using this indicator (distance between bid and ask), along with the size of the transaction, certain exemplary embodiments may use a regression analysis to calculate coefficients describing the transaction costs for individual bonds and categories of bonds. Certain embodiments may then use these coefficients to generate transaction cost adjusted prices for each trade to infer the mid-market. Furthermore, these embodiments may weight these transaction cost adjusted prices to create a current estimate of bond value.

Additionally, certain embodiments may use regression analysis to calculate coefficients that describe the relationship between a bond and selected ETFs. In the absence of new trades, the embodiments may update the valuation estimate by applying the coefficient adjusted ETF changes. As a result, the embodiments may produce bond evaluations in real-time and without human analysis.

More specifically, an exemplary aspect may comprise a computer system having one or more processors, comprising: a receiving component that receives valuation data for a security; a filtering component that filters the received valuation data to remove outlier values according to a predetermined set of parameters; a transaction cost adjustment component calculates a transaction cost adjustment coefficient based on a first transaction cost adjustment regression calculation of the processed valuation data, and determines a final transaction cost adjustment value based on the transaction cost adjustment coefficient; a market adjustment component that calculates a market adjustment coefficient based on a first market adjustment regression calculation of the processed valuation data, and determines a final market adjustment value based on the market adjustment coefficient; and an output component that outputs a pricing estimation of the security based on the final transaction cost adjustment value and the final market adjustment value.

In one or more exemplary system embodiments: (1) the pricing estimation is determined by rescaling prices to terms of the final transaction cost adjustment value and the final market adjustment value; (2) a confidence interval component calculates a confidence interval for the outputted pricing estimation; (3) the confidence interval is calculated with approximately the same frequency as the outputted pricing estimation; (4) the received valuation data comprises ETF transaction price data; (5) the received valuation data comprises bond attribute data; (6) the received valuation data comprises credit rating data; (7) the received valuation data comprises TRACE data; and/or (8) the pricing estimation is updated by applying one or more coefficient adjusted ETF data updates.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts an exemplary flowchart of real-time evaluated pricing for a corporate bond model.

FIG. 1B depicts an exemplary model pricing process.

FIG. 2 depicts an exemplary flow chart showing the work flow for an exemplary data preparation step.

FIG. 3 depicts a flow chart showing the work flow of an exemplary trade history calculation.

FIG. 4 depicts an exemplary flow chart of value estimation.

FIG. 5 depicts an exemplary workflow for the real model value estimation.

FIG. 6 depicts an exemplary timeline for when model price is triggered to be updated at some time T.

FIG. 7 depicts an exemplary menu.

FIG. 8 depicts an exemplary Investment Grade Worksheet Enhancements screen and a High Yield Worksheet Enhancements screen.

FIG. 9 depicts an exemplary Agency Worksheet screen.

FIG. 10 depicts exemplary Investment Grade and High Yield screens.

FIG. 11 depicts an exemplary trade data enhancement screen.

FIG. 12 depicts an exemplary model pricing configuration screen for data preparation.

FIG. 13 depicts an exemplary model pricing configuration screen for transaction cost adjustment.

FIGS. 14 and 15 depict exemplary model pricing configuration screens for market adjustment.

FIG. 16 depicts an exemplary graph of a 75-25 confidence interval.

FIG. 17 depicts an exemplary flowchart showing the logic of real-time process of model pricing Phase One and Phase Two, and the connection between the two phases.

FIG. 18 depicts an exemplary flow chart of a high level workflow of how to use model price in Market Data Ranking

FIG. 19 depicts an exemplary pricing mode displayed on a Model Details screen.

FIG. 20 depicts an exemplary Quotes Market Data screen for each system, i.e., IG, HY and AGY for display of model price and model evaluations.

FIG. 21 depicts an exemplary investment grade data ranking profile screen.

FIG. 22 depicts an exemplary Quote History screen for each system, i.e., IG, HY and AGY, displaying model price and model evaluations.

FIG. 23 depicts an exemplary event log.

FIG. 24 depicts an exemplary model pricing configuration screen for a confidence interval.

FIG. 25 depicts an exemplary model pricing configuration screen for a confidence group.

FIG. 26 depicts an exemplary sector configuration screen for model notifications.

FIG. 27 depicts an exemplary model pricing configuration screen for a confidence interval.

FIG. 28 depicts an exemplary sector configuration screen for model notifications.

FIG. 29 depicts an exemplary upload button.

FIG. 30 depicts an exemplary screen of upload blended price betas.

FIG. 31 depicts an exemplary new tab added on the screen of Security Details as “Blended Px Betas” and display CUSIP with 18 betas.

FIG. 32 depicts an exemplary computer network system.

DETAILED DESCRIPTION OF CERTAIN EXEMPLARY EMBODIMENTS

Exemplary embodiments described herein provide real-time model pricing of securities, e.g., corporate bonds, using past trade information, provide an automated confidence measure that allows the system or user to judge the reliability of model prices, and provide the functionality and controls necessary to use the model price in market data ranking as one of the data sources among quotes, trades and evaluations.

According to a first embodiment, i.e., Phase One, specifications for real-time model pricing of corporate bonds are provided. The first embodiment provides a model and the workflows for estimating the current value of a corporate bond using trade history, as well as movements in the general credit market as proxied by liquidly traded exchange traded funds. The mathematical framework underlying the model is described herein.

According to a second embodiment, i.e., Phase Two, business requirements for an automated gauge of model price reliability are provided, along with controls over using the model price alongside of related market input information.

1. Phase One Overview

Exemplary embodiments described herein support real-time model pricing of corporate bonds using past trade information. A model and workflows for estimating current value of a corporate bond using trade history, as well as movements in the general credit market as proxied by liquidly traded exchange traded funds, are provided. Also provided are mathematical settings for regressions in Appendix D. Exemplary regressions described herein fit into the framework described in Appendix D and one may identify components of the framework for each specific regression. “Right-hand-side” refers to quantities including observations of dependent variables. “Basis functions” refer to quantities including observations of independent variables. Except as otherwise stated, section numbers and appendices referred to within Phase One refer to Phase One section numbers and appendices.

• • 1.1 Basic Workflows

FIG. 1A depicts an exemplary flowchart of real-time evaluated pricing for a corporate bond model. FIG. 1B depicts an exemplary model pricing process. Model Pricing includes two basic processes:

• A daily (overnight) process that uses trade history and ETF data to create a value estimate for each security in the model.
• A real-time (intraday) process that updates the last value estimation as new trades and ETF prices arrive in the system.

Daily (Overnight) Processes: The pricing model has three components: transaction cost adjustment (TCA), market adjustment (MktA), and value estimation (VE). The three components of the model can be calculated in separate steps:

• At the end of each day, the system takes trade prices and adjusts them for transaction costs using information on their size and direction (e.g. dealer buys, interdealer, or dealer sells).
• Then the system takes transaction cost-adjusted prices and adjusts them for market movements since the time of the trade.
• After iterating the above two processes, the system then takes a history of transaction-cost and market-adjusted prices and constructs a value estimate.

Real-Time (Intraday) Process: For each day, at some specified time interval, updated market-wide indicators can be used to market-update all value estimates. In addition, when new trades occur in an issue at the start of day, these trades can be used in the value estimation model to update value estimates, allowing the real time model to be run in response to the periodic updating of ETF data and as trades occur.

• • 1.2 Securities in Scope

An exemplary model may include trade information of U.S. corporate bonds from TRACE data. For a security to be eligible to be included in the model, the security may:

• Be USD denominated
• Be TRACE eligible
• Have at least ‘n’ trades in a 3-year trade history, where ‘n’ is configurable (initially set to 6). n=6 is a reasonable starting point since it is the minimum requirement to calculate adjusted price in Section 3.6., while the professor currently requires 1000 trades.
• Not be a convertible bond, preferred stock, convertible preferred, or index linked note

2. Data Preparation

As described in this section, a data set is input into the system and filtered according to certain conditions, and a series of variables are created for use in further calculations. FIG. 2 depicts a flow chart showing the work flow for an exemplary data preparation step.

• • 2.1 Data Inputs
• ETF data. This data set contains the log of the most recent transaction price, and bid and ask as of a series of time stamped records. The tickers that are used in this model are LQD, HYG, IEI, and TLT. For Agencies, use ETF tickers AGZ instead of LQD, IEI-AGZ instead of HYG-LQD, and remain TLT-IEI the same.
  Noted: (1) For the time range of ETFs, the system may go back to whatever the last time range, regardless of how far it is. Thus, if there was a trade at 3 am, the system may use the most recent ETF closing price. If bond market was open but stock market was closed, the system use the most recent close price, which may be 1 day or 1.5 days ago.
• (2) For Fair Value, the system may avoid opening price. The system may use 9:30 snap (which may be the open or may be a few second later) and this is a better predictor of future prices than the local close. It may be that for bond trades occurring right around 9:30, it is better to append the 9:35 ETF prices.
• (3) The system may exclude the ETF suspect prices and instead use the ETF price 5 minutes before (or the most recent one).
• Bond attribute data. This data set contains the following variables that describe the bond features: Entity ID, CUSIP, maturity date, an issuer identifier, sector and pricing system (IG, HY or Agencies).
• Credit rating data. This data set contains S&P credit ratings for each issue at the time of data collection. For issues without S&P ratings, ratings are inferred from Moody's or Fitch ratings, or, if unrated, from the issue's yields. The system may include a mapping table of ratings between IDC rating bucket and the three agencies, see Appendix A for the mapping table and more details. For Agencies, there may be no credit difference for the credit line bucket and variable R may be removed from the model.
• TRACE data. The system uses trades from TRACE data, see Appendix B for more details about how the system obtains TRACE data by merging two files (not required for Omega).
  • 2.2 Holiday Calendar

Follow the same holiday schedule as IG/HY systems, i.e., a modified SIFMA calendar to include NYSE open days.

There are two scenarios on holiday:

• If ETF data comes in but no trade data since stock market is open while bond market is closed, then the system calculates new model price;
• If both stock and bond markets are closed, then no new model price is calculated.
  • 2.3 Data Cleaning
    2.3.1 Drop Outliers and Problematic Trade Observations

The system drops outliers and other likely problematic trade observations under the following circumstances, if:

• lotsize<$1000
• price<=0, price>160
• price is missing
• side is missing
• is suspect=“Y”
• special price=“Y”
  2.3.2 Drop Interdealer Paired Client Trades

An interdealer trade is identified as paired if it shares the same CUSIP, exact execution time, and lot size with a client trade (dealer buy or sell). Then client trades that are paired with interdealer trades are dropped, but the interdealer trade is retained.

2.3.3 Drop Cancelled or Replaced Trades from Estimation

Trades that are known to have been eventually cancelled or replaced are not used in any estimation, but these trades are retained in order to have transaction costs and betas appended to them. In other words, we drop cancelled and replaced trades in intraday processing, but keep them in tradeset prepared for overnight regression.

2.3.4 Drop Matured Bonds

Some matured bonds continue to be evaluated past their maturity date, either at par or at a fixed price, within continuous pricing. There is functionality built into the continuous pricing systems (EVAL, Omega) to manage this process. However, this functionality may not be replicated in the model, as the final output to the client is not the pure model prices. It is a combination of model prices, blended prices and continuous prices (see description of Model Pricing Phase Two section on functionality). If a bond does not have a model price, the system may send the continuous price. Therefore for matured bonds, if the system removes them from the model automatically at maturity, the existing continuous price functionality may take over and send the appropriate price (or absence).

Though the system may not produce a model price for matured (or called or defaulted) bonds, the system may include historical trades on these bonds in the input trade data to the overnight regressions. This is because the bonds were legitimately non-matured when the trades occurred, and therefore still form part of the history that the regressions may be using.

Intraday Model prices may be calculated for the universe of bonds which:

• (a) Have TRACE trades, and
• (b) Are not matured—OR—are matured but are in default

Overnight regression shall include matured securities which have TRACE trades within the TRADE-WINDOW (where the window is currently 4 years).

• • 2.4 Trade Data Processing
    2.4.1 Construct 30 Maturity * Credit Cells

Trades are divided into groups based on credit ratings and time to maturity. As high yield bonds with more than 10 years to maturity are rare, they are included in the 7.5-10 group. Thus, there are six credit rating groups (AA and above, A, BBB, B, and CCC or below) and five time-to-maturity groups (0-2 years, 2-5 years, 5-7.5 years, 7.5-10 years including 10-20 years and 20+ years).

The maturity * credit cells have the following format as the tables show. Table 1 is for Investment Grade bonds. Table 2 is for High Yield bonds.

TABLE 1
Investment Grade Maturity * Credit Grids

Maturity

	0-2	2-5	5-7.5	7.5-10	10-20	20+
Credit Ratings	YTM	YTM	YTM	YTM	YTM	YTM

AAA
AA
A
BBB

TABLE 2
High Yield Maturity * Credit Grids

Maturity

			5-7.5
Credit Ratings	0-2 YTM	2-5 YTM	YTM	7.5+ YTM
BB
B
CCC or worse

2.4.2 Note: The system uses the credit ratings to identify Investment Grade bonds and High Yield bonds, as shown in Table 1, HY bonds are the ones with ratings BB or below. So for HY indicator shown in the regression in later sections, HY indicator may be 1 if the bond has ratings BB or below, otherwise it is 0.
2.4.3 For agency bonds, only 6 cells for the different maturities are necessary and terms of credit ratings are dropped, as shown in Table 3.

TABLE 3
Agencies Maturity * Credit Grids
Maturity

0-2 Y	2-5	5-7.5	7.5-10	10-20	20+
TM	YTM	YTM	YTM	YTM	YTM

2.4.4 Note: To identify Agency and Corporate bonds, the bond's feed. If the trade comes from BTDS feed, it may be corporate; and if the trade is from ATDS feed, it may be agency.
2.4.5 Order Trades on Execution Time

Trades are ordered within each issue based on execution time. For cases with multiple trades executed in a given second, trades are ordered by IssuePriceID. The trade ordering is used for calculating the average of last 5 trades in Section 3.6.2.

2.4.6 Weight Observations on Time

Observations are weighted based on distance in time from the current date. The weight assigned to each is proportional according to the following equation:

weight = e today - date ⁢ ⁢ _ ⁢ ⁢ of ⁢ ⁢ _ ⁢ ⁢ trade 100 . ( 2.1 )

These weights are then divided by the sum of the expression in the following equation for the current and prior trade:

Adjusted ⁢ ⁢ Weights = Weight 0.8 + 0.3 * S z * ( 1 - ABS ⁡ ( S d + P ) 2 ) + 0.25 * ABS ⁢ ( S d ) - 0.15 * ( S d + P )

For trade with a size greater than $250,000, weights adjustment is multiplied by 5 for Dealer Buys.

2.4.7 Save Trades Records

To construct a baseline price in Section 3.6.2., transaction cost and market adjusted prices of trades from the last 5 CUSIP*seconds may be saved, i.e., trade t-1 to t-5. In order to half the memory and reduce the sample, the most recent X trades per CUSIP may be kept, since for thin bonds a longer past history is necessary. Performance improves with X until X hits about 5000. All trades may be saved from last year and the last 5000 trades older than 1 year. This reduces the sample by about 40%. Also, when calculating out of sample TCs and MAs for the issue-level scaling, if it's month t, keep all trades from t-1 to t-12, and then the 5000 most recent from t-13 to the beginning of the sample data.

2.4.8 Error Handling

The following describes how the system handles situations when certain parameters are missing. There are two possible exemplary scenarios of missing parameters:

• If a market level parameter(s) is (are) missing, the system may use the entire sets of coefficients from yesterday, and do the calculation with intraday trade information at real-time.
• If a bond level parameter(s) is (are) missing, the system may stop generating model pricing for that specific bond, and select continuous pricing mode instead.
• If some trade data or parameter(s) is (are) missing, the system may drop that trade for overnight regression, and count it as incomplete trade in the notifications.
  • 2.5 Input Variables Creation

A series of primitive input variables are defined with initialized value as shown in Table 4 (some contents are for agencies):

TABLE 4
Primitive Input Variables (from raw data)

	Variable	Input (in
	Name (in	Stata		Data
Objective	model)	code)	Description/Function	Identity
Price	p	p	Price in points (Par = 100)	Trade
Side Indicator	Sd	tt	tt = { 1 , if ⁢ ⁢ Dealer ⁢ ⁢ Sell 0 , if ⁢ ⁢ Interdealer - 1 , if ⁢ ⁢ Dealer ⁢ ⁢ Buy , one of the variables in Regression 1	Trade
Pair status indicator	P	dtt	dtt = { 1 , if ⁢ ⁢ interdealer ⁢ ⁢ trade ⁢ ⁢ that ⁢ ⁢ is ⁢ ⁢ paired ⁢ ⁢ with ⁢ ⁢ dealer ⁢ ⁢ sell 0 , if ⁢ ⁢ unpaired ⁢ ⁢ interdealer ⁢ ⁢ trades - 1 , if ⁢ ⁢ interdealer ⁢ ⁢ trade ⁢ ⁢ that ⁢ ⁢ is ⁢ ⁢ paired ⁢ ⁢ with ⁢ ⁢ dealer ⁢ ⁢ buy , one of the variables in Regression 1	Trade
Lotsize	lotsize	lotsize	Lotsize in $	Trade
Rescaled trade size	Sz	fq	fq = Max ⁡ ( 0 , Min ⁡ ( 1 , Ln ⁡ ( 1000000 lotSize ) Ln ⁡ ( 20 ) ) ) , one of the variables in Regression 1	Trade
Side	Sd * Sz	ttfq	TT * FQ, one of the variables in	Trade
indicator *			Regression 1
Rescaled
trade size
Paired	P * Sz	dttfq	DTT * FQ, one of the variables in	Trade
indicator *			Regression 1
Rescaled
trade size
Executed		dt	Execution Date-Time variable	Trade
Time
Reported		dt_report	The reported time of a trade; this is	Trade
Time			used to store date calculation results
Truncated		MAquantityindicator	This indicates if the reported TRACE	Trade
TRACE			quantity is truncated; and “E” for
Quantity			estimated if truncated and “A” for
Indicator			actual if not.
Primary		piid	Categorical variable; aggregated a few	Bond
instrument			cases of CUSIP or InstrumentID
ID			changes into a common identifier
Drop		a	a = 1 if ultimately cancelled (Created	Trade
indicator			by Eric; used for tracking cancelled
			trades)
Group ID		piida	Grouping of combinations of PIID and	Bond
			A (in TC model, all A = 1 observations
			are dropped, so this maps one-to-one
			to PIID)
Trade		n	Trade identifier (Created by Eric; used	Trade
identifier			for disassembling and reassembling
			datasets)
			Note: Tradeset is ordered in increasing
			piid and n. may not be required, but
			may be included for Regression 7.
Numbers		n1	Numbers trades within values of	Trade
trades in			PIIDA, in order of execution time
PIIDA			(with ties broken by values of n) (used
			for counting the numbers trades with
			values of piida)
Numerical		SPrat	Numerical version of S&P rating	Bond
S&P			(AAA = 20, AA+ = 19, BB+ = 10,
rating			CCC+ = 4, CCC = 3, CC = 0, D = −12)
Integer		intSP	Rating used to put bonds into the 30	Bond
S&P			cells, intSP = int((SPrat + 1)/3)
rating			Special Cases: (1) SPrat = 0
			(corresponds to CC) and below may
			have intSP = 1 (the same as SPrat = 2-
			4);
			(2) SPrat = 20 (the
			AAAs) gets intSP = 6 (the same as
			AA− to AA+)
			Please see Appendix A for conversion
			between SPrat and intSP.
Rating	R	rat	Rating = 0 for bonds rated AA+ or	Bond
			above, 1 for bonds rated CC or below,
			and is linear in credit rating between as
			(S&P numerical − 3)/16, i.e., rat = 1-
			max(0, min(1, (SPrat − 3)/16)). R may be
			set to 0 in calculation of Agencies.
Year to		ytm	Years to Maturity from execution date,	Trade
Maturity			the formula is (maturity_date-
			execution_date)/365.25
Issue-		iytm	Year to maturity that is used to	Bond
Level			calculate maturity * credit cells, i.e.,
Year to			the issue-level ytm
Maturity
Maturity	YTM15	mat15	mat15 = min(max(0, ytm), 15)/10,	Trade
(15 years)			which is mat15 = 1 for bonds 15
			years or more from maturity, 0 for
			bonds at maturity, and is linear in time
			to maturity in between
Maturity	YTM10	mat10	mat10 = min(max(0, ytm), 10)/10,	Trade
(10 years)			which is mat10 = 1 for bonds 10
			years or more from maturity, 0 for
			bonds at maturity, and is linear in time
			to maturity in between
Year and		yrmo	Year month variable (January 2009 =	Trade
month			200901)
Month		yq	Groups months in the data (November 2008 =	Trade
Group			107, June 2012 = 150)
			The minimum value for yq is
			configurable.
Number		m	1 to N numbering of months appearing	Trade
of months			in data , may be started from 1 and
			increasing by 1, no hole
Recent	lnHYG	lnHYG	Most recent ln(HYG total return index)	Trade
log HYG			as of execution time
total
return
Recent	lnIEI	lnIEI	Most recent ln(IEI total return index)	Trade
log IEI			as of execution time
total
return
Recent	lnLQD	lnLQD	Most recent ln(LQD total return index)	Trade
log LQD			as of execution time
total
return
Recent	lnTLT	lnTLT	Most recent ln(TLT total return index)	Trade
log TLT			as of execution time
total
return
Recent	lnAGZ		Most recent ln(AGZ total return index)	Trade
log AGZ			as of execution time
total
return
Side = +1 indicator	I1S(Sd)	ttpos	ttpos = { 1 , if ⁢ ⁢ S d = 1 0 , otherwise , one of the variables in Regression 1	Trade
Paired = +1 indicator	I1P(P)	dttpos	dttpos = { 1 , if ⁢ ⁢ P = 1 0 , otherwise , one of the variables in Regression 1	Trade
Side = +1	Sz × I1S	ttposfq	ttpos * fq, one of the variables in	Trade
Indicator *			Regression 1
Size
Paired	Sz × I1P	dttposfq	dttpos * fq, one of the variables in	Trade
Indicator *			Regression 1
Size
Maturity *	R × YTM15	mat15rat	mat15 * rat	Trade
Rating
Side *	Sd × R	ttrat	tt * rat, one of the variables in	Trade
Rating			Regression 1
Side *	Sd × YTM15	ttmat15	tt * mat15, one of the variables in	Trade
Maturity			Regression 1
Side = +1	I1S × R	ttposrat	ttpos * rat, one of the variables in	Trade
Indicator *			Regression 1
Rating
Side = +1	I1S × YTM15	ttposmat15	ttpos * mat15, one of the variables in	Trade
Indicator *			Regression 1
Maturity
Side *	Sd × Sz × R	ttfqrat	ttfq * rat, one of the variables in	Trade
Size *			Regression 1
Rating
Side *	Sd × Sz × YTM15	ttfqmat15	ttfq * mat15, one of the variables in	Trade
Size *			Regression 1
Maturity
Side *	Sd × Sz × R × YTM15	ttfqmat15rat	ttfq * mat15 * rat, one of the variables	Trade
Size *			in Regression 1
Maturity *
Rating
Paired	P × Sz × R	dttfqrat	dttfq * rat, one of the variables in	Trade
indicator *			Regression 1
Size *
Rating
Paired	P × Sz × YTM15	dttfqmat15	dttfq * mat15, one of the variables in	Trade
indicator *			Regression 1
Size *
Maturity
Paired	P × Sz × R × YTM15	dttfqmat15rat	dttfq * mat15 * rat, one of the	Trade
indicator *			variables in Regression 1
Size *
Maturity *
Rating
Side = +1	I1S × Sz × R	ttposfqrat	ttpos * fq * rat, one of the variables in	Trade
Indicator *			Regression 1
Size *
Rating
Side = +1	I1S × Sz × YTM15	ttposfqmat15	ttpos * fq * mat15, one of the variables	Trade
Indicator *			in Regression 1
Size *
Maturity
Side = +1	g21 × R	ttposfqmat15rat	ttpos * fq * mat15 * rat, one of the	Trade
Indicator *			variables in Regression 1
Size *
Maturity *
Rating
Paired =	I1P × Sz × R	dttposfqrat	dttpos * fq * rat, one of the variables in	Trade
+1			Regression 1
Indicator *
Size *
Rating
Paired =	I1P × Sz × YTM15	dttposfqmat15	dttpos * fq * mat15, one of the	Trade
+1			variables in Regression 1
Indicator *
Size *
Maturity

In order to calculate differences in regression equations, additional series of variables are created as the shown in Table 5.

TABLE 5
Additional Variables (for regression use)

	Variable	Input (in
	Name (in	Stata		Data
Inputs	model)	code)	Description/Function	Identity
Adjusted Weights	w	w	weight = e - today - date ⁢ ⁢ _ ⁢ ⁢ of ⁢ ⁢ _ ⁢ ⁢ trade 100 Adjusted ⁢ ⁢ Weights = ( Weight ) 0.8 + 0.3 * S Z * ( 1 - ABS ⁡ ( S d + P ) 2 ) + 0.25 * ABS ⁢ ( S d ) - 0.15 * ( S d + P ) Note: The weights are defined here, but in an exemplary embodiment may be used and created in the first difference calculation in the regression	Trade

2.5.1 Input Data Requirements
Provided below are descriptions of some input data requirements in Table 4:

• piid and n: Tradeset is ordered in increasing piid and n. This may not be required by the method, but may be utilized in Regression 7.
• m may start from 1 and increasing by 1 consecutively unless some months are missing. It's not necessary to start from November 2008, i.e., November 2008=1, however, m may be set starting from 1 and increasing by 1 as months moving forward. There can be a hole if a month is missing. A safe guard may be added by java code to detect missing months.
• The calculation formula of yq is yq=(Y−2000)×12+M, where Y is the year of “dt” and M is the month of “dt”. The minimum value of “yq” is configurable, i.e., it's not necessary to be a fixed number. yq is not related to m. Also, a safe guard may be added on holes (if any) in yq that can accommodate missing months.
• The creation and use of n1 can be described by three STATA commands:
  • Sort piida dt n
  • qby piida: replace (gen) n1=_n
  • tsset piida na

The system recreates n1 for Regression 7, i.e., value estimation, because: 1) some values in old “n1” may be eliminated by requiring “dt” being after May 2009; 2) some records with different old “n1” values may be merged by “collapse (sum). . . ” But the system may also create n1 using the same algorithm used in the model (from Regression 1 to Regression 7), and this algorithm is consistent with the STATA code. Note: n1 is consistent from the step2 file through the rest of the transaction cost model. Between the step1 and step2 files, some observations may be dropped and n1 renumbered to keep consecutive (this is data prep stage). The regressions begin after step2 is saved and then reloaded the STATA code, and n1 is consistent until trades are collapsed to the CUSIP*second level in value estimation. Within each value of piida, n1 is the observation number when they are ordered by execution time and then n, which is an observation used to disassemble and reassemble the data. Ordering it by n with execution time ensures that ties are always broken the same way.

3. Model

This section describes how calculate the three components of the model are calculated in detail.

• • 3.1 Transaction Cost Adjustment

FIG. 3 depicts a flow chart showing the work flow of an exemplary trade history calculation, which can be separated into two parts: transaction cost adjustment and market adjustment.

3.1.1 Regression 1: Calculate In-sample and Out-of-sample Transaction Costs

The trade-to-trade change in price Δp is regressed on the trade-to-trade changes in a series of variables designed to capture transaction costs. A single regression is run including all bonds and all trades from the prior 24 months. Observations are weighted as described in 2.4.3.

3.1.1.1. Basis functions: Variables Designed to Capture Transaction Costs in Regression 1

Excluding constant term, the number of basis functions is 24 (M=24, see Appendix E). The system identifies basis functions for Regression 1 as follows, omitting time dependency for state variables for saving typing:

g₁(t_i, . . . )=S_d

g₂(t_i, . . . )=P

g₃(t_i, . . . )=S_d×S_z

g₄(t_i, . . . )=P×S_z

g₅(t_i, . . . )=S_z

g₆(t_i, . . . )=I₁^S

g₇(t_i, . . . )=I₁^P

g₈(t_i, . . . )=S_z×I₁^S=g₅×g₆

g₉(t_i, . . . )=S_z×I₁^P=g₅×g₇

g₁₀(t_i, . . . )=S_d×R=g₁×R

g₁₁(t_i, . . . )=S_d×YTM₁₅=g₁×YTM₁₅

g₁₂(t_i, . . . )=I₁^S×R=g₆×R

g₁₃(t_i, . . . )=I₁^S×YTM₁₅=g₆×YTM₁₅

g₁₄(t_i, . . . )=S_d×S_z×R=g₁×g₅×R

g₁₅(t_i, . . . )=S_d×S_z×YTM₁₅=g₁×g₅×YTM₁₅

g₁₆(t_i, . . . )=S_d×S_z×R×YTM₁₅=g₁₅×R

g₁₇(t_i, . . . )=P×S_z×R=g₄×R

g₁₈(t_i, . . . )=P×S_z×YTM₁₅=g₄×YTM₁₅

g₁₉(t_i, . . . )=P×S_z×R×YTM₁₅=g₁₈×R

g₂₀(t_i, . . . )=I₁^S×S_z×R=g₁₂×S_z

g₂₁(t_i, . . . )=I₁^S×S_z×YTM₁₅=g₈×YTM₁₅

g₂₂(t_i, . . . )=g₂₁×R

g₂₃(t_i, . . . )=I₁^P×S_z×R=g₅×g₇×R

g₂₄(t_i, . . . )=I₁^P×S_z×YTM₁₅=g₅×g₇×YTM₁₅

f_j(t_i, . . . )=g_j(t_i, . . . )−g_j(t_i−1, . . . ), j=1, . . . , 24

3.1.1.2. The Right-hand-side of the Regression

The right-hand-side for this regression includes the 1st differences of prices. This regression is run on rolling 24-month windows of data. Coefficients from the regression run using data from t−24 months to t are applied to the variables in 3.1.1.1. from trades from month t, to yield an in-sample predicted transaction cost for each trade, see formula (3.1) below. They are also applied to the variables from trades from month t+1 to yield and out-of-sample predicted transaction cost, see formula (3.2) below.

3.1.1.3. Outputs: Transaction Costs Calculation

The output from this step is an in-sample and out-of-sample predicted transaction cost that may be appended to every past trade in the dataset. In addition, the betas from the most recent rolling window may be retained so they can be applied to newly arrived trades in real-time. The formula for in-sample transaction cost calculation is as follows:

C I ⁢ _ ⁢ Origina ⁢ l ⁡ ( t ) = ∑ j = 1 24 ⁢ ⁢ β j ⁡ ( t ) × g j ⁡ ( S d ⁡ ( s ) , P ⁡ ( s ) , S z ⁡ ( s ) , R ⁡ ( s ) , YTM 15 ⁡ ( s ) ) s ≤ t ( 3.1 )

The formula for out-of-sample transaction cost calculation is as follows:

C O ⁢ _ ⁢ origina ⁢ l ⁡ ( t ) = ∑ j = 1 24 ⁢ ⁢ β j ⁡ ( t ) × g j ⁡ ( S d ⁡ ( s ) , P ⁡ ( s ) , S z ⁡ ( s ) , R ⁡ ( s ) , YTM 15 ⁡ ( s ) ) s > t ( 3.2 )

Both in-sample and out-of-sample predicted transaction costs are truncated to have a minimum of 5 basis points, and a maximum of 2.5 times a regression coefficient obtained from a simple version of the regression above, estimated in the same window as the following formula:
C_o=Sign(S_d+P) * max(0.05, min(2.5 * coef,Sign(S_d+P) * C_{O_original})), if ABS(S_d+P)=1   (3.3)
C_I=Sign(S_d+P) * max(0.05, min(2.5 * coef,Sign(S_d+P) * C_{I_original})) if ABS(S_d+P)=1   (3.4)

This last coefficient (coef) is obtained by regressing price changes on the first nine basis functions. The variables with ‘pos’ in the names may all be zero for dealer buys, resulting in five actual basis functions. And the system may take the coefficient on Side * Size, which is β₃ in the equation above, thus coef=β₃.

3.1.2 Regression 1 for Agency Bonds

3.1.2.1. Basis functions for Agency Bonds

For agencies, the model in 3.1.1.1. may lose some terms that involved credit and becomes a 16 parameter model with basis functions identified (M=15, see Appendix D) as the following:

g₁(t_i, . . . )=S_d

g₂(t_i, . . . )=P

g₃(t_i, . . . )=S_d×S_z

g₄(t_i, . . . )=P×S_z

g₅(t_i, . . . )=S_z

g₆(t_i, . . . )=I₁^S

g₇(t_i, . . . )=I₁^P

g₈(t_i, . . . )=S_z×I₁^S=g₅×g₆

g₉(t_i, . . . )=S_z×I₁^P=g₅×g₇

g₁₀(t_i, . . . )=S_d×YTM₁₅=g₁×YTM₁₅

g₁₁(t_i, . . . )=I₁^S×YTM₁₅=g₆×YTM₁₅

g₁₂(t_i, . . . )=S_d×S_z×YTM₁₅=g₁×g₅×YTM₁₅

g₁₃(t_i, . . . )=P×S_z×YTM₁₅=g₄×YTM₁₅

g₁₄(t_i, . . . )=I₁^S×S_z×YTM₁₅=g₈×YTM₁₅

g₁₅(t_i, . . . )=g₁^P×S_z×YTM₁₅=g₅×g₇=YTM₁₅

f_j(t_i, . . . )=g_j(t_i, . . . )−g_j(_i−1, . . . ), j=1, . . . , 15

3.1.2.2. The Right-Hand-Side for Agency Bonds

The same as in 3.1.1.2, right-hand-side for Agency bonds includes 1^st differences of prices.

3.1.2.3. Outputs for Agency Bonds

Keep the rest the same as in 3.1.1.3., and change equations (3.1) and (3.2) into

C I ⁢ _ ⁢ Origina ⁢ l ⁢ _ ⁢ agy ⁡ ( t ) = ∑ j = 1 15 ⁢ ⁢ β j ⁡ ( t ) × g j ⁡ ( S d ⁡ ( s ) , P ⁡ ( s ) , S z ⁡ ( s ) , YTM 15 ⁡ ( s ) ) s ≤ t ( 3.5 ) C O ⁢ _ ⁢ origina ⁢ l ⁢ _ ⁢ agy ⁡ ( t ) = ∑ j = 1 15 ⁢ ⁢ β j ⁡ ( t ) × f j ⁡ ( S d ⁡ ( s ) , P ⁡ ( s ) , S z ⁡ ( s ) , YTM 15 ⁡ ( s ) ) s > t ( 3.6 )

• • 3.2 Market Adjustment
    3.2.1 Regression 2: Calculate Out-of-sample Market Adjustment

The trade-to-trade change in price is regressed on the in-sample predicted transaction cost and several other variables capturing trade-to-trade changes in ETF prices and their interactions with bond characteristics.

3.2.1.1. Basis Functions: Variables Designed to Capture ETF Price Changes in Regression 2

Excluding constant term, the number of basis functions is 18 (M=18, see Appendix E). The system may omit time dependency for state variables as before but also may include it whenever necessary. Basis functions are more complex due to the 1st difference involvement. Basis functions may be identified as follows:

g₁(t_i, . . . )=1n(LQD), f₁(t_i, . . . )=g₁(t_i, . . . )−g₁(t_i−1, . . . )

f₂(t_i, . . . )=f₁×YTM₁₀(t_i)

f₃(t_i, . . . )=f₁×R(t_i)

f₄(t_i, . . . )=f₁×YTM₁₀(t_i)×R(t_i)

f₅(t_i, . . . )=f₁×H(t₁)

f₆(t_i, . . . )=f₅×R(t_i)

f₇(t_i, . . . )=f₅×YTM₁₀(t_i)

f₈(t_i, . . . )=f₇×R(t_i)

g₉(t_i, . . . )=1n(HYG)−1n(LQD), f₉(t_i, . . . )=g₉(t_i, . . . )−g₉(t_i−1, . . . )

f₁₀(t_i, . . . )=f₉×YTM₁₀(t_i)

f₁₁(t_i, . . . )=f₉×R(t_i)

f₁₂(t_i, . . . )=f₉×YTM₁₀(t_i)×R(t_i)

f₁₃(t_i, . . . )=f₉×H(t_i)

f₁₄(t_i, . . . )=f₁₃×R(t_i)

f₁₅(t_i, . . . )=f₁₃×YTM₁₀(t_i)

f₁₆(t_i, . . . )=f₁₅×R(t_i)

g₁₇(t_i, . . . )=1n(TLT)−1n(IEI), f₁₇(t_i, . . . )=[g₁₇(t_i, . . . )+g₁₇(t_i−1, . . . )]×YTM₂₀(t_i, . . . )×I_A(t_i), where

I_A is A-rating or better indicator

f₁₈(t_i)=C_{I_Original}(t_i)−C_IOriginal(t_i−1)

H(t) is the high yield indicator that equals to 1 if it is high yield, otherwise it is 0.

3.2.1.2. The Right-hand-side of the Regression

The right-hand-side also includes 1st differences in prices.

3.2.1.3. Outputs: Out-of-sample Betas and Out-of-sample Market Adjustments

Coefficients from the data are used to estimate three betas for each bond, an LQD beta, an HYG-LQD beta, and a TLT-IEI beta. Let the three beta multipliers produced by the regression above (at the end of the repression window) be β_LQD(t), β_HYG-LQD(t), and β_TLT-IEI(t) respectively. The beta is the sum of the coefficients multiplied by the relevant variable (divided by the ETF change) as follows:

β LQD ⁡ ( t ) = ∑ j = 1 8 ⁢ ⁢ β j ⁡ ( t ) ⁢ f j ⁡ ( s ) s > t f 1 ⁡ ( s ) s > t ( 3.7 ) β HYG - LQD ⁡ ( t ) = ∑ j = 9 16 ⁢ ⁢ β j ⁡ ( t ) ⁢ f j ⁡ ( s ) s > t f 9 ⁡ ( s ) s > t ( 3.8 )
β_TLT-IEI(t)=β₁₈(t)×YTM₂₀(s)_s>t×R_A(s)_s>t, for all bonds rated better than A and in 20 years of YTM, β_TLT-IEL(t)=0 otherwise.   (3.9)

The betas are then used out-of-sample to construct predicted market adjustments from one trade to the next from month t-24 to t-1. Then the out-of-sample market adjustment at t is calculated as follows:
M_o(t,s)=β_LQD(t)×(1n(LQD(s))1n(LQD(s−1))) +β_HYG-LQD(t)×(1n(HYG(s))−1n(LQD(s))−1n(HYG(s−1))+1n(LQD(s−1)))+, s>t β_TLT-IEI(ln(TLT(s))−1n(IEI(s))−1n(TLT(s−1))+1n(IEI(s−1)))   (3.10)
3.2.2 Regression 2 for Agency Bonds

3.2.2.1. Basis Functions for Agency Bonds

For agencies, the model in 3.2.1.1. may lose some terms that involved credit and becomes a 11 parameter model, also by using LQD and HYG-LQD take AGZ and IEI-AGZ instead as the following:

g₁(t_i, . . . )=1n(AGZ), f₁(t_i, . . . )=g₁(t_i, . . . )−g₁(t_i−1, . . . )

f₂(t_i, . . . )=f₁×YTM₁₀(t_i)

f₃(t_i, . . . )=f₁×H(t_i)

f₄(t_i, . . . )=f₃×YTM₁₀(t_i)

g₅(t_i, . . . )=1n(IEI)−1n(AGZ), f₅(t_i, . . . )=g₅(t_i, . . . )−g₅(t_i−1, . . . )

f₆(t_i, . . . )=f₅×YTM₁₀(t_i)

f₇(t_i, . . . )=f₅×H(t_i

f₈(t_i, . . . )=f₇×YTM₁₀(t_i)

• g₉(t_i, . . . )=1n(TLT)−1n(IEI), f₉(t_i, . . . )=[g₉(t_i, . . . )−g₉(t_i−1, . . . )]×YTM₂₀(t_i)
  f₁₀(t_i)=C_{I_Original}(t_i)−C_{I_Original}(t_i−1)

3.2.2.2. The Right-hand-side for Agency Bonds

The same as in 3.2.1.2, right-hand-side for Agency bonds includes 1^st differences of prices.

3.2.2.3. Outputs for Agency Bonds

Keep the rest the same as in 3.2.1.3., and change equations (3.7), (3.8) and (3.9) into the following:

β AGZ ⁡ ( t ) = ∑ j = 1 4 ⁢ ⁢ β j ⁡ ( t ) ⁢ f j ⁡ ( s ) s > t f 1 ⁡ ( s ) s > t ( 3.11 ) β IEI - AGZ ⁡ ( t ) = ∑ j = 5 8 ⁢ ⁢ β j ⁡ ( t ) ⁢ f j ⁡ ( s ) s > t f 5 ⁡ ( s ) s > t ( 3.12 )
β_TLT-IEI(t)=β₉(t)×YTM₂₀(s)_s>t, for all bonds in 20 years of YTM, it is 0 other-wise.   (3.13)

And the calculation of out-of-sample market adjustment changes into the following:
M_{O_agy}(t,s)=β_AGZ(t)×(1n(AGZ(s))−1n(AGZ(s−1)))+β_IEI-AGZ(t)×(1n(IEI(s))−1n(AGZ(s))−1n(IEI(s−1))+1n(AGZ(s−1)))+β_TLT-IEI(t)×(1n(TLT(s))−1n(IEI(s))1n(TLT(s−1))+1n(IEI(s−1)))   (3.14)

• • 3.3 Transaction Cost and Betas for Maturity*Credit Cells

This section is to run regressions that estimate transaction cost and beta multipliers for each of 30 maturity* credit cells. For each of the 30 cells and each of the rolling windows, three regressions below are run.

3.3.1 Regression 3: Calculate In-sample Predicted Value

3.3.1.1. Basis Function: Changes in Out-of-sample Predicted Transaction Costs from Regression 1

• The sole basis function is ΔC_O=C_O(t_i)−C_O(t_i−1) from Regression 1 formula (3.2) and truncated by formula (3.3).
• The right-hand-side is again the price change Δp

3.3.1.2. Regression Equation

The first regression is a regression of trade-to-trade price changes on changes in out-of-sample predicted transaction costs from Regression 1. Therefore, this regression is a weighted line-fit calculated as follows:
Δp=β₀^P+β₁^P·ΔC_O   (3.15)
3.3.2 Regression 4: Calculate In-sample Beta

3.3.2.1. Basis Function: Trade-to-trade Change in Ln(LQD)

• The sole basis function is Δ1n(LQD)
• The right-hand-side is Δp−β₁^P·ΔC_O

3.3.2.2. Regression Equation

The second regression is a regression of trade-to-trade price changes (less the in-sample predicted value from Regression 3) on the trade-to-trade change in Ln(LQD).

This regression is weighted line-fit calculated as follows:
Δp−β₁^P=β₀^l+β₁^l·Δ1n(LQD)   (3.16)
3.3.3 Regression 5: Calculate CO and SE for a Bond's Cell

3.3.3.1. Basis Function: Trade-to-trade change in ETFs and In-sample Beta

• The sole basis function is Δ1n(HYG)−Δ1n(LQD)
• The right-hand-side is Δp−β₁^P·ΔC_o−0.5·β_LQDΔ1n(LQD)−0.5·β₁^l·Δ1n(LQD)
  Here β_LQD is from the 3.2.1.3., see formula (3.7).

3.3.3.2. Regression Equation

The third regression is a regression using the dependent variable from Regression 4, less the trade-to-trade in LQD times the average of the in-sample beta from the second regression and the LQD beta estimated in 3.2.1.3. This regression is the weighted line-fit calculated as follows:
Δp−β₁^PΔC_O−0.5·β_LQD·Δ1n(LQD)−0.5·β₁^l·Δ1n(LQD)=β₀^h+β₁^h·[Δ1n(HYG)−Δ1n(LQD)]  (3.17)

3.3.3.3. Outputs: Standard Error for Bond's Cell

The details on standard error for coefficients are included in Appendix E. In addition, both coefficients and standard errors from the above three regressions are recorded for each cell and rolling window. Once the transaction cost and market adjustments are calculated in step 3.4. for time period T, the coefficients from the rolling window T-24 to T-1 can be discarded. All the coefficients for all 30 cells and ˜40 rolling windows may be calculated, and then all the adjustments may be calculated. All 30 cell's coefficients for window T-24 to T-1 may also be calculated along with the adjustments for T, and then move onto the next rolling window. New rolling windows are determined every day, and thus 50 sets of coefficients instead of 24 are calculated over a 24-month past history.

3.3.4 Regression 3, 4, 5 for Agency Bonds

3.3.4.1. Regression 3 for Agency Bonds

Steps and equations are the same as in section 3.3.1.

3.3.4.2. Regression 4 for Agency Bonds

Change ETF LQD into AGZ in each equation of section 3.3.2., and keep other calculations the same.

3.3.4.3. Regression 5 for Agency Bonds

Replace HYG-LQD by IEI-AGZ in each equation of section 3.3.3., and also use β_AGZ instead of β_LQD in related calculations.

• • 3.4 Blend TCA and MktA with Bond's Cell CO and SE

In this section, estimated transaction costs and credit market betas from 3.1. and 3.2. are blended with those estimated in 3.3.

3.4.1 Blend of the CO for Bond's Cell

Cell-average transaction cost, cell-average betas, and cell-average standard error are calculated and then blended with outputs from TC model and Market Adjustment Model to produce blended transaction cost and blended betas. Let (ytm,R) be maturity-rating pair. For each calculation, the performance of this step occurs as follows:

• 1. Identify surrounding maturity-rating cells for (ytm,R) (see below for details).
• 2. Calculate surrounding cell-weights (see below for details).
• 3. Calculate surrounding-cell-averaged (with the weights calculated at last step) coefficients and standard errors: β₁^P, Ē_P, β₁^l, Ē_l, β₁^h, and Ē_h. All these quantities depend on (ytm,R).

This step is just for smoothing each cell-dependent quantity.

Calculate the global cell-average coefficients and standard errors over all 30 cells (averaging the results from the 3^rd step). Since the 3^rd step may not been implemented, this step is simply averaging “simple” results of cell-restricted regressions. For saving typing, we use the same notations for surrounding-cell-averages.

The three outputs are calculated as follows (using results from previous step):

• 1. Transaction costs: tc=C_o·(1+(β₁^P−1)·(0.8−0.3·max(0,min(1,100·Ē_P−100)), C_o is from (3.5). The output may be just C_o if Ē_P>0.1 or |β₁^P−1|>0.5.
• 2. LQD Beta: β_l=max(5,0.4·(β_LQD+β₁^l)).
• 3. HYG-LQD Beta:
  β_h=0.8·β_HYG-LQD+0.8·(B₁^h−β_HYG-LQD)·(1−0.2·max(0,min(4,Ē_h))).

The adjacent cells are identified as follows. Given a point of pair of YTM and credit rating, the first thing to do is to identify adjacent cells. This is done according to its location relative to cell midpoints. Let {R_i}_i=1⁶ be the set of credit ratings. Currently R₁ represents CCC or below, R₆ represents AA and above. Let {YTM_i}_i=0⁶ be the set of midpoints of time-to-maturity ranges. Currently YTM₀=0, YTM₁=1, YTM₂=3.5, YTM₃=6.5, . . . , YTM₆ represents 20+years. Given a point P=(R,Y) rating bounds and maturity bounds are determined for P i.e. R_i and R_i+1 such that R_i≤R≤R_i+1; YTM_j and YTM_j+1 such that YTM_j≤Y≤YTM_j+1. The adjacent cells for P may be the combination of rating bounds and maturity bounds. Note that either ranges [R_i,R_i+1] and [YTM_j, YTM_j+1] may shrink to a point, in that case the combination may have less than 4 cells.

Cell weight calculations are outlined as follows. There are two components to be calculated: YTM weight and credit rating weight. The YTM weight is calculated as

w YTM =  Y - YTM k  YTM j + 1 - YTM j ,
given that the range └YTM_j, YTM_j+1┘ didn't shrink. Here Yϵ└YTM_j, YTM_j+1┘ and k=j or j+1 depending on which adjacent cell is calculating weight. The credit rating weight is calculated in similar manner where

w R = d ⁡ ( R , R k ) n i , i + 1 , n i , i + 1
is the distance between R_i and R_i+1 given the range didn't shrink. Here Rϵ[R_i,R_i+1] and d(R,R_k) is distance between R and R_k, k=i or i+1 depending on which adjacent cell we are calculating weight. Distance between two credit ratings means the number upgrades (downgrades) needed traveling from one rating to the other. The cell weight is then the product of credit rating weight and YTM weight:
w_C=w_YTM×w_R.
3.4.2 Blend of the CO for Agency Bonds

For agencies, 6 cells for the different maturities may be used and the coefficients from the 2 cells with nearest midpoints are blended.

3.4.3 Blend the Average of the Cell CO

For transaction costs, the out-of-sample predicted transaction cost from 3.1. is transformed into the rescaled transaction cost by the following equation:
tc=C_o·(1+(β₁^P−1)*(0.8−0.3* Max(0,Min(1,Ē_P* 100−100))))   (3.18)
If the standard error is: Ē_P>0.1 or |β₁^P−1|>0.5, then the cell-average coefficient CO_Ais discarded and the out-of-sample transaction cost from 3.1., C_O, is used instead.
3.4.4 Calculate New Betas

3.4.4.1. Calculate the new LQD Beta
β_l=Max(5,β_LQD*0.4+B₁^l*0.4)   (3.19)
For agencies, slightly change equation (3.19) into:
β_α=Max(5,β_AGZ*0.4+β₁^l* 0.4)   (3.20)
Calculate the new HYG-LQD Beta
β_h=β_HYG-LQD * 0.8+0.8 *(β₁^h−β_HYG-LQD) * (1−0.2 * max(0, min(4, Ē_h)))   (3.21)
For agencies, slightly change equation (3.21) into:
β_i=β_IEI-AGZ * 0.8+0.8 * (β₁^h−β_IEI-AGZ) * (1−0.2* max(0, min(4, Ē_h)))   (3.22)

3.4.4.2. Calculate the new TLT-IEI Beta

The TLT-IEI beta is simply retained from 3.2.1.3., formula (3.9):

β m = ⁢ β TLT - IEI = ⁢ { β 17 * YTM 20 * R A , for ⁢ ⁢ all ⁢ ⁢ bonds ⁢ ⁢ rated ⁢ ⁢ better ⁢ ⁢ than ⁢ ⁢ A - ⁢ and ⁢ ⁢ in ⁢ ⁢ 20 ⁢ ⁢ years ⁢ ⁢ of ⁢ ⁢ maturity 0 , for ⁢ ⁢ all ⁢ ⁢ bonds ⁢ ⁢ rated ⁢ ⁢ less ⁢ ⁢ than ⁢ ⁢ A - ⁢ or ⁢ ⁢ within ⁢ ⁢ 10 ⁢ ⁢ years ⁢ ⁢ of ⁢ ⁢ maturity

For agencies, use formula (3.13) instead.

3.4.5 Calculate New Market Adjustment
etf2(t, s)=β_l(t)×(1n(LQD(s))−1n(LQD(s−1)))+β_h(t)×(1n(HYG(s))−1n(LQD(s))−1n(HYG(s−1))+1n(LQD(s−1)))+β_m(t)×(1n(TLT(s))−1n(IEI(s)) l−1n(TLT(s−1))+1n(IEI(s−1)))   (3.23)

And for agency bonds, change equation (3.23) into:
etf2(t, s)=β_{1_agy}(t)×(1n(AGZ(s))−1n(AGZ(s−1)))+β_{h_agy}(t)×(1n(IEI(s))−1n(AGZ(s))−1n(IEI(s−1))+1n(AGZ(s−1))) β_m(t)×(1n(TLT(s))−1n(IEI(s))−1n(TLT9s−1))+1n(IEI(s−1)))   (3.24)

• • 3.5 Calculate Final TCA and MktA
    The final output of this section is a trade history with transaction costs and market adjustments adjusted by multipliers calculated from the above steps.
    3.5.1 Regression 6: Calculate CO and SE for TCA and MktA

3.5.1.1. Basis Functions: Trade-to-trade Price Change, Trade-to-trade Change in Estimated TC and MktA

• The two basis functions are Δtc and etf2
• The right-hand-side is Δp

3.5.1.2. Regression Equation

Rolling window regressions are run for each issue. Regressions are only run for 24-month windows with at least 20 trades. The trade-to-trade price change is regressed on the trade-to-trade change in estimated transaction costs and the trade-to-trade market adjustment.

This regression is the weighted line-fit:
Δp={tilde over (β)}₀+{tilde over (β)}₁ * w * Δtc+{tilde over (β)}₂* w * etf2   (3.25)

3.5.1.3. Outputs: TCA and MktA Coefficients and Standard Errors

Coefficients and standard errors are recorded for the transaction cost and market adjustments as CO_TCA, CO_MktA and SE_TCA, SE_MktA. Let {tilde over (β)}₁ and {tilde over (β)}₂ be the two coefficients:
CO_TCA(t)={tilde over (β)}₁(t)   (3.26)
CO_MktA(t)={tilde over (β)}₂(t)   (3.27)
3.5.2 Calculate Final Transaction Cost Adjustment (TCA)

The final transaction cost adjustment is calculated as the step 12 adjustment tc multiplied by the factor as:

tc 3 = tc * ( 1 + ( β 1 ~ - 1 ) * max ⁡ ( 0 , min ⁢ ⁢ ( 1 , 0.5 - 0.25 * ln ⁢ ⁢ ( 8 * σ 2 ⁡ ( β 1 ~ ) ) ) ) ) ( 3.28 )
3.5.3 Calculate Final Market Adjustment (MktA)

Similarly, the final market adjustment is calculated using the step 12 betas multiplied by the factor as:

etf ⁢ ⁢ 23 = etf ⁢ ⁢ 2 * ( 0.9 * ( 1 + ( β 2 ~ - 1 ) * max ⁡ ( 0 , min ⁡ ( 1 , 1 - 3 * σ 2 ⁡ ( β 2 ~ ) ) ) ) ) ( 3.29 )

• • 3.6 Value Estimation

FIG. 4 depicts an exemplary flow chart of value estimation. In general, value estimation occurs in three steps:

• Trades are reduced to the CUSIP * trade level and the average characteristics of trades executed during that second are calculated. Rescale all prices to current terms of transaction cost adjusted and market adjusted.
• Construct a rolling average value estimate, where the valuation goes as:
  new average=(new adjusted price) * w+(1−w) * (old average)
• The rolling average is calculated and then recalculated in two iterations.
  3.6.1 Reduce and weight trades to CUSIP * Second

3.6.1.1. Calculate TCA and MktA for Each Trade

For each trade, calculate a transaction cost adjustment by using formula (3.28), and a trade-to-trade market adjustment, using betas from Regression 6 in 3.5. multiplied by changes since the last trade. Cumulate the trade-to-trade market adjustments into a cumulative index. Transaction cost adjustment can be obtained by following steps below:

• i. From overnight regression—Regression 1, the system may save 24 coefficients, β_j, j=1, . . . , 24. When a new trade comes in, using each coefficient times its related trade/bond feature variable, and then sums them up as:
  C_{O_original}=β₁ * S_d+β₂ * P+β₃ * S_d * S_z+β₄ * P * S_z+β₅ * S_z+β₆ * +I₁^S+β₇ * I₁^P+β₈ * S_z * I₁^S+β₉ * S_z * I₁^P+β₁₀ * S_d * R+β₁₁ * YTM₁₅+β₁₂ * I₁^S * R+β₁₃ * I₁^S * YTM₁₅+β₁₄ * S_d * S_z * R+β₁₅ * S_d * S_z * YTM₁₅+β₁₆ * S_d * S_z * R * YTM₁₅+β₁₇ * P * S_z * R+β₁₈ * P * S_z * YTM₁₅+β₁₉*P*S_z*R*YTM₁₅+β₂₀*I₁^S*S_z*YTM₁₅+β₂₂*I₁^S*S_z* R * YTM₁₅+β₂₃ * I₁^P * S_z * R+β₂₄ * I₁^P * S_z * YTM₁₅
• ii. By using the same trade feature variables, the truncation is calculated of out-of-sample predicted transaction costs by the following equation:
  C_o(t)=Sign(S_d(t)+P(t)) * max(0.05,min(2.5 * coef(t),Sign(S_d(t)+P(t)) * C_{O_original}(t))) , if ABS(S_d(t)+P(t))=1
  where coef(t)=β₃(t), which is from nine-parameter TC regression in Regression 1
• iii. For each bond, by using the maturity * credit cells, blend the truncated out-of-sample predicted transaction costs generated above with cell coefficients from Regression 3-5:
  tc=C_o·(β₁^p−1) * (0.8−0.3 * Max(0,Min(1,Ē_p * 100−100)))) C_o is from Section 3.1.1.

β₁^p, Ē_p are coefficients from Regression 3-5

• iv. For each bond, use tc from the above times the issue-level multiplier to obtain the final transaction cost adjustment tc3:

tc 3 = tc * ( 1 + ( β 1 ~ - 1 ) * max ⁡ ( 0 , min ⁢ ⁢ ( 1 , 0.5 - 0.25 * ln ⁢ ⁢ ( 8 * σ 2 ⁡ ( β 1 ~ ) ) ) ) )
tc is from Section 3.4.3.

β 1 ~ , σ 2 ⁡ ( β 1 ~ )
are coefficients from Regression 6

Market adjustments are calculated using betas generated from overnight regression—Regression 2. Using these betas times, the ETF price changes and sums them up as the following steps shows:
etf2(t, s)=β_l×(1n(LQD(t))−1n(LQD(s)))+β_h×(1n(HYG(t))−1n(LQD(t))−1n(HYG(s))+1n(LQD(s)))+β_m×(1n(TLT(t))−1n(IEI(t))−1n(TLT(s))+1n(IEI(s)))   i.
where t is the time when a new trade comes in and triggers the model to update, while s is last model updated time

• ii. Market adjustments are adjusted by issue-level multiplier as:

etf ⁢ ⁢ 23 = etf ⁢ ⁢ 2 * ( 0.9 * ( 1 + ( β 2 ~ - 1 ) * max ⁡ ( 0 , min ⁡ ( 1 , 1 - 3 * σ 2 ⁡ ( β 2 ~ ) ) ) ) )

β 2 ~ , σ 2 ⁡ ( β 2 ~ )
are coefficients from Regression 6

3.6.1.2. Weight Trades by Executed Second

Trades are weighted by log trade size. Use

ln ⁡ ( Lotsize 100 ) ,
where lotsize is par value in dollars or use variable MAquantityindicator to weight the trades. For each CUSIP * second, a weighted average of data is determined for all trades executed that second, including the replace or cancelled ones.
Variables to be averaged:

• Transaction cost adjusted price.
• Interdealer trade indicator variable.
• Unpaired interdealer trade indicator variable.
• Log size.
• Investment grade indicator.
• Side+Paired.
  Variables to be needed but may not vary within CUSIP * second:
• Cumulative market adjustment.
• Date and Time.
  3.6.2 Construct a Rolling Average Value Estimate

3.6.2.1. Construct a Baseline Price

For a bond with trades at {t_i, i=1,2, . . . , k} during the 6 month window, use tc3 and etf23 developed above from Section 3.5.2. and 3.5.3., after weighted average if necessary, calculated as follows: P_adj(t_i)=P(t_i)−tc3(t_i), i=1,2, . . . , k. Use the average of transaction cost and market adjusted prices from the last 5 CUSIP * seconds with trades.

Define the baseline price as:

P ⁢ ⁢ 5 adj ⁢ ( t i ) = P adj ⁡ ( t i ) + P adj ⁡ ( t i - 1 ) + P adj ⁡ ( t i - 2 ) + P adj ⁡ ( t i - 3 ) + P adj ⁡ ( t i - 4 ) 5 ( 3.30 )
Define Y=P_adj(t_i+1)−P5_adj(t_i−1)−MktA(t_i−5,t_i)−etf23(t_i+1)   (3.31)
And: X=P_adj(t_i)−P5_adj(t_i−1)−MktA(t_i−5, t_i)   (3.32)
where:
MktA(t_i−5, t_i)=etf23(t_i)+0.8 * etf23(t_i−2)+0.6 * etf23(t_i−2)+0.4 * etf23(t_i−3)+0.2 * etf23(t_i−4)   (3.33)
For Y only, trades that are eventually cancelled or replaced may not be considered.

3.6.2.2. Regression 7: Calculate the Prediction of the Next Trade Price

• • Variable definition:
    • I_d: Interdealer indicator
    • U_d: Unpaired interdealer indicator
    • T_d1: The log differences in time between trade t+1 and t
    • T_d2: The log differences in time between trade t and t−1
    • IG_d: Investment grade indicator
    • T_s: The average trade size
    • I: The indicator variable for trade t and t−1 occurring on the same calendar day
    • Sum: The sum of Side and Paired
  • Inputs
    • The independent variable is
      • f₁(X, . . . )=X
      • f₂(X, . . . )=X * I_d=f₁ * I_d
      • f₃(X, . . . )=X * U_d=f₁ * U_d
      • f₄(X, . . . )=X * T_d1=f₁ * T_d1
      • f₅(X, . . . )=X * T_d2=f₁ * T_d2
      • f₆(X, . . . )=X * IG_d=f₁ * IG_d
      • f₇(X, . . . )=X * T_s=* f₁ * T_s
      • f₈(X, . . . )=X * Sum=f₁ * Sum
      • f₉(X, . . . )=X * Sum=f₁ * Sum
    • The dependent variable is Y
  • Regression Equation:

Y = A · β = ∑ j = 1 9 ⁢ β j × a j ( 3.34 )
Where:

• • A is a N×9 matrix with entry a_j=f_j(X, . . . ) we recognizes that A is the design matrix.
    • β is a 9×1 column vector of coefficients.
    • Observations are equal weighted
  • Outputs: Save the coefficients from this regression
  • Rolling window: For this regression, 6 month window is a sufficient length.

This regression produces one month ahead out-of-sample estimate, which is calculated as

Y ^ = ∑ j = 1 9 ⁢ ⁢ β * x ,
as well as one month ahead out-of-sample estimate is obtained as PredPrice(t_i)=P5_adj(t_i−1)+MktA(t_i−6, t_i−1)+Ŷ. During daily real-time evaluation, when new trades come in, the above calculation is repeated and the process is shown in Section 4.6.4., PredPrice(t_i) is one way of mixing tc3 and etf23 to produce a model evaluation for time t_i.

3.6.2.3. Construct Prediction of the Next Trade Price

The coefficients from the above regression are used out of sample to construct a prediction of the next trade price as of each trade. Also, let Δt, the difference between t+1 and t, equal to one second. And save the coefficients from the last rolling window for use out-of-sample.

• 3.6.3 Repeat the Process for Rolling Average
  • 3.6.3.1. Iterate the Processes for New Baseline Price

In this step, 3.6.2. is repeated. For each iteration, the new baseline price is the predicted next-trade price as of trade t−1. And Y is the difference between the baseline price and trade t+1's transaction cost and market-adjusted prices in formula (3.31), and X is the difference between the baseline price and the predicted next-trade price as of trade t as in formula (3.32). Regression 7 is run to generate predicted next-trade prices as in formula (3.34), and save coefficients from the last rolling window for real-time use.

3.6.3.2. Average the Predicted Next-trade Price

When the predicted next-trade price is averaged from the first and second iterations, a 50-50 ratio is used out-of sample as a measure of current value, adjusted for market movements since the last trade using the betas.

3.6.4 Outputs of Value Estimation

To take into the real time model, outputs from the above steps of value estimation are determined as follows:

• • For each bond
    • The predicted next-trade price from the most recent CUSIP * second with a trade.
    • The ETF values from the time of that trade.
    • The betas estimated in 3.4.
    • The coefficients used for transaction cost adjustment.
    • The coefficients from both iterations from the most recent rolling window.
  • 3.7 Summary of Outputs in Section 3

Table 6 is a summary of outputs which are used in Section 4 for real time value estimation; Table 7 is the mapping of variable names used for calculation in real-time process in Section 4.

Contents in each column are listed below:

• • Objective describes calculation purpose, i.e., what variable is calculated here.
  • Variable Name (in model) is the name used in mathematical function.
  • Output (in Stata code) is the variable name in STATA coding and Methodology may use in Math Library coding.
  • Regression No./Function shows where the variable appears.
  • Coefficient Name is the name that the output name Methodology might use when they generate the coefficients from regression equations
  • Data Identity shows whether the variable is a trade data or a bond level data Related Sections shows the section where the variable is generated and used, TC—Transaction Cost Adjustment, MA—Market Adjustment, VE—Value Estimation, RT—Real Time Process.

TABLE 6
Outputs from Section 3

Variable Name

Output (in

Regression

Data

Related Sections

Objective	(in model)	Stata code)	No./Function	Coefficient Name	Identity	TC	MA	VE	RT
Original	CO_original	py3 (then	Regression 1	Reg1_Coef_tt,	Market	√			√
out-of-		replaced	(3.2)	Reg1_Coef_dtt,
sample		by the		Reg1_Coef_ttfq,
predicted		truncated		Reg1_Coef_dttfq,
transaction		transaction		Reg1_Coef_fq,
costs		cost py3		Reg1_Coef_ttpos,
without		below)		Reg1_Coef_dttpos,
truncated				Reg1_Coef_ttposfq,
				Reg1_Coef_dttposfq,
				Reg1_Coef_ttrat,
				Reg1_Coef_ttmat15,
				Reg1_Coef_ttposrat,
				Reg1_Coef_ttposmat
				15,
				Reg1_Coef_ttfqrat,
				Reg1_Coef_ttfqmat15,
				Reg1_Coef_ttfqmat15
				rat,
				Reg1_Coef_dttfqrat,
				Reg1_Coef_dttfqmat
				15,
				Reg1_Coef_dttfqmat
				15rat,
				Reg1_Coef_ttposfqrat,
				Reg1_Coef_ttposfqmat
				15,
				Reg1_Coef_ttposfqmat
				15rat,
				Reg1_Coef_dttposfqrat,
				Reg1_Coef_dttposfqm
				at15
For Agency:	CO_original_agy		Regression 1	Reg1agy_Coef_tt,	Market	√			√
Original			(3.6)	Reg1agy_Coef_dtt,
out-of-				Reg1agy_Coef_ttfq,
sample				Reg1agy_Coef_dttfq,
predicted				Reg1agy_Coef_fq,
transaction				Reg1agy_Coef_ttpos,
costs				Reg1agy_Coef_dttpos,
without				Reg1agy_Coef_ttposf
truncated				q,
				Reg1agy_Coef_dttpos
				fq,
				Reg1agy_Coef_ttmat
				15,
				Reg1agy_Coef_ttpos
				mat15,
				Reg1agy_Coef_ttfqm
				at15,
				Reg1agy_Coef_dttfqm
				at15,
				Reg1agy_Coef_ttposfq
				mat15,
				Reg1agy_Coef_dttpos
				fqmat15
Truncated	CO	Py3	Regression 1	Reg1_Coef9_ttfq	Market	√			√
out-of			(3.3)
sample
transaction
cost
Cell-	β1p	BldReg3_		BldReg3_Coef_spy3	Bond
average		Coef_spy3
coefficient
CO
Cell-	Εp	BldReg3_		BldReg3_Se_spy3	Bond
average		Se_spy3
standard
error SE
Final LQD	βl	beta_l	Regression 2	βLQD is generated from	Bond		√
Beta			(3.7)	Regression 2 (betaL1):
calculated			Regression 4	Reg2_Coef_sLQD,
by using			(3.16)	Reg2_Coef_sLQDmat
βLQD and			(3.19)	10,
the cell-				Reg2_Coef_sLQDrat,
average				Reg2_Coef_sLQDmat
coefficient				10rat,
β1l				Reg2_Coef_sLQDhy,
				Reg2_Coef_sLQDhy
				rat,
				Reg2_Coef_sLQDmat
				10hy,
				Reg2_Coef_sLQDmat
				10hyrat,
				β1l is generated from
				Regression 4(col):
				Reg4_Coef_sLQD
For Agency:	βa	beta_a	Regression 2	βAGZ is generated from	Bond		√
Final AGZ			(3.11)	Regression 2:
Beta			Regression 4	Reg2agy_Coef_sAGZ,
calculated			(3.20)	Reg2agy_Coef_sAGZ
by using				mat10,
βAGZ and				Reg2agy_Coef_sAGZ
the cell-				hy,
average				Reg2agy_Coef_sAGZ
coefficient				mat10hy,
β1a				β1l is generated from
				Regression 4:
				Reg4agy_Coef_sAGZ
Final	βh	beta_h	Regression 2	βHYG-LQD is generated	Bond		√
HYG-LQD			(3.8)	from Regression 2
Beta			Regression 5	(betaH1):
calculated			(3.17)	Reg2_Coef_sHL,
by using			(3.21)	Reg2_Coef_sHLhy,
βHYG-LQD				Reg2_Coef_sHLrat,
and the cell-				Reg2_Coef_sHLhyrat,
average				Reg2_Coef_sHLmat
coefficient				10,
β1h				Reg2_Coef_sHLmat
				10hy,
				Reg2_Coef_sHLmat
				10hyrat
				β1h is generated from
				Regression 5 (coh):
				Reg4_Coef_sHL
For Agency:	βi	beta_i	Regression 2	Reg2agy_Coef_sIA,	Bond		√
Final IEI-			(3.12)	Reg2agy_Coef_sIAhy,
AGZ Beta			Regression 5	Reg2agy_Coef_sIAm
calculated			(3.22)	at10,
by using				Reg2agy_Coef_sIAm
βIEI-AGZ				at10hy
and the cell-
average
coefficient
β1i
Final TLT-	βm	beta_m	Regression 2	Reg2_Coef_sLM10a	Bond		√
IEI Beta,			(3.9)
remained
as the same
as the
original
TLT-IEI
Beta
For Agency:	βm_agy	beta_m	Regression 2	Reg2agy_Coef_sLM	Bond		√
Final TLT-			(3.13)	10a
IEI Beta,
remained
as the same
as the
original
TLT-IEI
Beta
Issue-level		copi	Regression 6	Reg6_Coef_stc	Bond	√
transaction			(3.25)
cost
coefficient
Issue-level		sepi	Regression 6	Reg6_Se_stc	Bond	√
transaction			(3.25)
cost
standard
error
Issue-level		coe	Regression 6	Reg6_Coef_seft2	Bond		√
market			(3.25)
adjustment
coefficient
Issue-level		see	Regression 6	Reg6_Se_etf2	Bond		√
market			(3.25)
adjustment
standard
error
Market	(0.9 * (1 + ( − 1) *	emult	(3.29)	coe, see	Bond		√		√
adjustment	max(0, min(1,1 − 3 *
multiplier	)))
estimated
from COE
Estimated	Ŷ	py	Regression 7	Reg7_Coef_x,	Trade			√	√
value of Υ			(4.5)	Reg7_Coef_udx,
by using the				Reg7_Coef_dx,
coefficients				Reg7_Coef_xLnft,
times				Reg7_Coef_xLnt,
variables				Reg7_Coef_xfq,
coming with				Reg7_Coef_xig,
the trades				Reg7_Coef_xsame,
				Reg7_Coef_xpos
New	Ŷ2	py	Regression 7	Reg72-Coef_x2,	Trade			√	√
estimated			(4.8)	Reg72-Coef_x2ud,
value of Υ2				Reg72-Coef_x2Lnft,
by using the				Reg72-Coef_x2Lnt,
overnight				Reg72-Coef_x2fq,
coefficients				Reg72-Coef_x2ig,
times				Reg72-Coef_x2pos
variables
coming with
the trades

TABLE 7
Variables Mapping for Section 4

Variable Name

Output

Regression

Data

Related Sections

Objective	(in model)	(in Stata code)	No./Function	Coefficient Name	Identity	TC	MA	VE	RT
Large dealer	ldb	ldb		py3, cop, sep	Trade	√			√
buy
transaction
cost
Issue-level	ldb2	ldb2		tc, copi, sep	Trade	√			√
large dealer
buy
transaction
cost
Rescaled	tc	tc	Regression 5	py3, cop, sep	Trade	√			√
transaction			(3.18)
cost
Final	tc3	tc3	(3.28)	tc, copi, sep	Trade	√			√
transaction
costs
adjustment
Rescaled	etf2	etf2	Regression 5	beta_1, sLQD,	Bond		√		√
market			(3.23)	beta_h, sHL,
adjustment				beta_m, sLM10a
Final market	eft23	etf23	(3.29)	etf2, emult	Bond		√		√
adjustment
Adjusted	Padj	adjp		adjp = price − tpred2
price
Baseline	P5adj	adjp5	Regression 7	adjp5 = (adjp +	Trade			√
price			(3.30)	l.adjp +l2.adjp +
				13.adjp + 14.ajdp)/5
Interdealer	Id	dealer	Regression 7	dx = x * dealer	Trade			√
indicator			(3.34)	Reg7_Coef_dx
Unpaired	Ud	udealer		udx = x * udealer	Trade			√
interdealer				Reg7_Coef_udx
indicator
Log	Td1	ln(fs.dt/1000)	Regression 7	xlnft = x *	Trade			√
differences			(3.34)	ln(fs.dt/1000)
in time				Reg7_Coef_xLnft
between
trade t + 1
and t
Log	Td2	ln(s.dt/1000)	Regression 7	xlnft = x *	Trade			√
differences			(3.34)	ln(s.dt/1000)
in time				Reg7_Coef_xLnt
between
t and t − 1
Investment	IGd	Sprat > 10	Regression 7	xig = x * (Sprat > 10)	Trade			√
grade			(3.34)	Reg7_Doef_xig
indicator
Average	Ts	w/trades	Regression 7	xfq = X * w/trades	Trade			√
trade size			(3.34)	Reg7_Coef_xfq
The	I	dofc(dt)==dofc(l.dt))	Regression 7	xsame = x *	Trade			√
indicator			(3.34)	(dofc(dt)==dofc(l.dt))
variable for				Reg7_Coef_xsame
trade t and
t − 1
occurring
on the same
calendar
day
Sum of Slide	Sum	pos	Regression 7	xpos = x * pos	Trade			√
and Paired			(3.34)	Reg7_Coef_xpos	Trade			√
Difference	X	x	Regression 7	adjp, etfpred2, adjp5,
between the			(3.32)	cetfpred2
baseline
price and the
predicted
next-trade
price as of
trade t
Difference	Y	y	Regression 7	Reg7_Coef_x,	Trade			√
between the			(3.31)	Reg7_Coef_udx
baseline				Reg7_Coef_dx
price and				Reg7_Coef_xLnft
trade t + 1's				Reg7_Coef_xfq
transaction				Reg7_Coef_xig
cost and				Reg7_Coef_xsame
market-				Reg7_Coef_xpos
adjusted
prices
Estimated	Ŷ	py	Regression 7		Trade			√	√
value of Y			(4.5)
by using the
coefficients
times
variables
coming with
the trades
Prediction	PredPrice(t)	pprice	Regression 7	adjp5, etfpred2	Trade			√	√
of			(4.6)
transaction
cost and
market
adjusted
price
New	X2	x2	Regression 7	pprice	Trade			√	√
difference			(4.7)
between the
baseline
price and the
predicted
next-trade
price
New	Y2	y2	Regression 7	Note: adjp, pprice,	Trade			√	√
difference				etfpred2
between the				Reg72_Coef_x2,
baseline				Reg72_Coef-x2ud,
price and				Reg72_Coef-x2Lnft,
trade t + 1's				Reg72_Coef-x2fq,
transaction				Reg72_Coef-x2ig
cost and				Reg72_Coef-x2pos
market-
adjusted
prices
New	Ŷ2	py2	Regression 7		Trade			√	√
estimated			(4.8)
calue of Y2
by using the
overnight
coefficients
times
variables
coming with
the new
trades
New	PredPrice2	pprice2	Regression 7	pprice, etfpred2, py2	Trade			√	√
prediction of			(4.9)
transaction
cost and
market-
adjusted
prices
Model Bid	Model Bid Price	mbid	(4.11)	Model Mid Price,	Trade			√	√
Price		(this variable may		ldb (or ldb2 or ldb3)
		not be included in
		coding)
Model Mid	Model Mid Price	mmid	(4.10)	pprice, pprice 2	Trade			√	√
Price		(this variable may
		not be included)
Model Ask	Model Ask Price	mask	(4.12)	Model Mid Price,	Trade			√	√
Price		(this variable may		Model Bid Price
		not be included)

4. Daily Real-Time Process

The real time model value estimation may be run in response to three triggers—new trades, cancelled/replaced trades, or in response to ETF price changes. FIG. 5 depicts an exemplary workflow for the real model value estimation.

The logic of the above process is as the following:

• • At the beginning of each day, use overnight regression (Regression 1, Regression 3, Regression 6) to calculate ldb (tc for large dealer buy only) and Idb2 (tc3 for large dealer buy only), by setting variables of trade features S_d=−1, S_z=0, and p=0 (In Stata code, the variables are set as tt=−1, fq=0, dtt=0). ldb and ldb 2 are calculated regardless of whether a large dealer buy trade to transaction cost adjusted is obtained, and they are used to generate bid model price from the mid model price. Calculation details are described in Section 4.4.
  • At the beginning of each day, overnight regression may be used—Regression 2 to calculate out-of-sample betas, and blend these betas with cell-level betas. Save these ETF betas for calculation of market adjustments and keep betas consistent intraday. Betas calculations are in Section 4.5.
  • Model pricing is updated in the following two scenarios:
    • New Trades: When a new trade comes in, the value estimation model may be updated with the new trade features, i.e., using coefficients from overnight regression to multiply the trade feature variables and calculate transaction cost adjusted prices, drop paired trades, and calculate market adjusted prices (Note: no need to run any regression in real-time process). Also, to determine if cancelled/replaced trades occur, and if so, update the value estimation model as if triggered by a new trade. Calculation details are in Section 4.6..
    • ETF Price Changes: When ETF price changes, the transaction costs adjustment keeps the same, and only market adjustment may be updated by adding the updated market adjustment to the most recent value estimate, i.e., the most recent model mid-price. Calculation details are in Section 4.7..
  • With tc and market-adjusted trade prices updated when the above two scenarios occur, these adjusted trade prices are used to generate model bid/mid/ask price together with Idb or ldb2 which have been calculated in the first step.
    Details and calculation methods of the above process is described in the following sections.
  • 4.1 Minimum Requirements of Intraday Calculation

Intraday Model prices are to be calculated for the universe of bonds which:

• • (a) Have TRACE trades, and
  • (b) Are not matured—OR—are matured but are in default

Overnight regression includes matured securities which have TRACE trades within the TRADE-WINDOW (where the window is currently 4 years). To calculate the first model price, at least six trades may be used to run the overnight regression. And to generate model price at real-time, besides these six trades, the seventh trade may need to happen the next day to trigger the intraday calculation on model price. For example, there are several possible cases:

• With at least six trades today, and the overnight regression is run by using these trades and saving the coefficients. The next day, calculate the first model price cannot be calculated until a new trade comes in.
• With at least six trades today, and the overnight regression is run by using these trades and saving the coefficients. The next day, there may not be a new trade but the ETF price changes. In this case, the first model price still cannot be calculated.
• The first model price may only be calculated when there is at least six trades today, and the overnight regression is run by using these trades and save the coefficients. With the seventh trade the next day (or several days later), the coefficients to generate the first model price can be used.
  • 4.2 Collapse Trades to CUSIP*Second Level

Trades are reduced to the CUSIP*second level. Calculate the average characteristics of trades executed each second, for each CUSIP. For each CUSIP*second, take a weighted average of data for all trades executed that second (including those that are eventually replaced or cancelled). Trades are weighted by

ln ⁡ ( Lotsize $100 ) .
The variables to be averaged are:

• Transaction cost adjusted price.
• Interdealer trade indicator variable.
• Unpaired interdealer trade indicator variable.
• Log size—See Section—4.6.4.4. for calculation details as variable “Average Trade Size.”
• Investment grade indicator.
• Side+Paired.
  Variables that are needed but may not vary within CUSIP*second are:
• Cumulative market adjustment.
• Date and Time.
  4.2.1 Aggregated Trade Variables

As shown above, trades are reduced to the CUSIP*second level. If multiple trades occurred in one second, results of aggregated trade are published within that second, i.e., weight-averaged aggregation of all trades in that second. Here is the list of the aggregated trade variables:

• Transaction cost adjusted price: calculated in Section 4.4.4.2. by using the weight 1n(lotsize/$100).
• Aggregated trade price: when trade price is displayed on the bond-level screen, it may be the aggregated trade price, i.e., weight-averaged trade price of all the trades in that second.
• Trade-to-trade price change: this is calculated by using aggregated trade price on CUSIP*second level.
• Model price: there is only one model price for each second and trades are aggregated before calculating model price.
  • 4.3 Overnight Regression Run

There are seven additional parameters used an exemplary overnight regression code, which are based on input variable “yq”:

• int minM—the minimum of month for regression rolling window and available regression coefficients. This is the minimum value for “yq”, currently it is 109. To provide room for regression, minM may be at least two months later than the 1^st data available month, e.g., if the 1^st month in which data is available is 107(=1+106) then minM may be at least 109. And minM is configurable.
• int fromM—the smallest “yq” value for over-night regression run e.g. 109. It can be greater than 109 but cannot be smaller than 109.
• int toM—the largest “yq” value for over-night regression run e.g. 150.
• int outputMktM—value of month the regression coefficients are required. It is usually the same value as “toM” i.e. the latest regression coefficients. (month-index for market level coefficients)
• int outputBndM—month-index for bond level coefficients
• m1Reg7—month-index for Regression 7 step 1 coefficients
• m2Reg7—month-index for Regression 7 step2 coefficients
  Calculation and relationship of the above seven additional parameters:
• minM=min(yq)
• fromM=min(yq)
• toM=max(yq)
• outputMktM=max(yq)
• outputBndM=max(yq)
• m1Reg7=max(yq)
• m2Reg7=max(yq)
  • 4.4 Calculate ldb and ldb2

ldb and ldb2 may only be updated once daily, i.e., ldb and ldb2 may be calculated at the beginning of each day and keep them the same the rest of the day regardless of whether a new trade is obtained during the day or whether there is large dealer buy trade intraday. ldb and ldb2 can be generated by the following sections. ldb and ldb2 are special case for tc and tc3, i.e., they are tc and tc3 only for large dealer buy trades. So the base calculation and formula used are the same as to tc and tc3, for large dealer buy trades, some of the terms may be zero and cancelled in the calculation.

4.4.1 Calculate Out-of sample Transaction Cost

From overnight regression—Regression 1, 24 coefficients have been saved:

β_j, j=1, . . . , 24. Set the values of all trade feature variables in the regression equation as:

• S_d=−1 (tt=−1)
• S_z=0 (fq=0)
• P=0 (dtt=0)
• I₁^s32 0 (ttpos=0)
• I₁^P=0 (dttpos=0)
  For each bond, using each coefficient times its related trade/bond feature variable, and then sums them up as (this equation has been simplified from equation (3.2) by plugging in the above variables to cancel several terms):
  C_Ooriginal=−Reg1_Coef_tt −Reg1_Coef_ttrat * R −Reg1_Coef_ttmat15 * YTM₁₅

4.4.1.1. Truncate Out-of-sample Transaction Cost

Keep the trade feature variables constant as:

• S_d=−1 (tt=−1)
• S_z=0 (fq=0)
• p=0 (dtt=0)
• I₁^s=0 (ttpos=0)
• I₁^P=0 (_dttpos=0)
  Calculate the truncation of out-of-sample predicted transaction costs by the following equation:
  C_o=(−1) * max(0.05,min(2.5 * Reg1_Coef9_ttfq, −C_{O_original}))
  where Reg1_Coef9_ttfq is from the nine-parameter TC regression in Regression 1 (Take regression of the first nine independent variables, and use the coefficient on Side * Size)

4.4.1.2. Blend the Cell Coefficients (Calculate ldb)

For each bond, by using the maturity * credit cells, blend the truncated out-of-sample predicted transaction costs generated above with cell coefficients from Regression 3:
ldb=C_O * (1+(BldReg3_Coef_spy3−1) * (0.8−0.3 * Max(0,Min(1,BldReg3_Se_spy3 * 100 −100 ))))
C_O is from the above, Section 4.4.2.
BldReg3_Coef_spy3 and BldReg3Se_spy3 are cell-average coefficient and standard error blended with Regression 3 Coefficient/Standard Error and the bond's cell weightings.

4.4.1.3. Calculate Final Transaction Cost Adjustment (Calculate Idb2)

For each bond, use tc from the above times the issue-level multiplier to obtain the final transaction cost adjustment tc3:
ldb2=Idb * (1+(Reg6_Coef_stc−1) * max(0, min(1,0.5−0.25 * 1n(8 * Reg6_Se_stc)))) ldb is from the above, Section 4.4.3.
Reg6_Coef_stc and Reg6_Se_stc are coefficient and standard error from Regression 6.

• • 4.5 Calculate Betas

From overnight regression—Regression 2, 18 coefficients have been saved:

β_j, j=1, . . . , 18. Use these coefficients to calculate out-of-sample betas at the beginning of each day, and keep them consistent on intraday trades. Please see Appendix F for calculation details, ETF betas may be generated overnight. These Bond Betas may be used to calculate market adjustments, i.e., etf2 and etf23, in Section 4.6. and Section 4.7.. Bond Betas (beta_1, beta_m, beta_h) may also be needed in Model Pricing Phase Two for calculation of squared change of etf2 and etf23.

• • 4.6 Updating in Response to New Trades
    4.6.1 Calculate Transaction Cost Adjustment

After a new trade or group of new trades occurs, the prices are transaction cost adjusted using the coefficients from the transaction cost model, i.e., Regression 1. Calculate the transaction cost adjustment by using the coefficients from overnight regression, multiplying the new trade features and summing them up. The process is similar as ldb and ldb2 calculation in Section 4.4., and the only difference is new trade feature variables are used in the calculation, instead of setting their values into constants.

4.6.2 Calculate Out-of-sample Transaction Cost

From overnight regression—Regression 1, saved 24 coefficients have been saved: β_j, j=1, . . . , 24. When a new trade comes in, using each coefficient times its related trade/bond feature variable, and then sums them up as:
C_Ooriginal=Reg1_Coef_tt * S_d +Reg1_Coef_dtt * P +Reg1_Coef_ttfq * S_d * S_z +Reg1_Coef_dttfq * P * S_z +Reg1_Coef_fq * S_Z +Reg1_Coef_ttpos * I₁^S +Reg1_Coef_dttpos * I₁^P +Reg1_Coef_ttposfq * S_z * I₁^{S +Reg}1_Coef_dttposfq * S_z * I₁^{P +Reg}1_Coef_ttrat * S_d * R +Reg1_Coef_ttmat15 * S_d * YTM₁₅ +Reg1_Coef_ttposrat * I₁^S* R +Reg1_Coef_ttposmat15 * I₁^S *YTM₁₅ +Reg1_Coef_ttfqrat * S_d * S_z* R +Reg1_Coef_ttfqmat15 * S_d*S_z*YTM₁₅ +Reg1_Coef_ttfqmat15rat * S_d*S_z* R * YTM₁₅ +Reg1_Coef_dttfqrat * P * S_z * R +Reg1_Coef_dttfqmat15 * P * S_z * YTM₁₅ +Reg1_Coef_dttfqmat15rat * P * S_z * R * YTM₁₅ +Reg1_Coef_ttposfqrat * I₁^S* S_z * R +Reg1_Coef_ttposfqmat15 * I₁^S* S_z * YTM₁₅ +Reg1_Coef_ttposfqmat15rat * I₁^S * S_z * R * YTM₁₅ +Reg1_Coef_dttposfqrat * I₁^P * S_z * R +Reg1_Coef_dttposfqmat15 * I₁^P * S_z * YTM₁₅
4.6.3 For Agencies: Calculate Out-of-sample Transaction Cost

For Agencies, the 15 parameter regression model is used in Regression 1, instead of the 24 parameter in IG/HY as above, i.e., β_j, j=1, . . . , 15. The 15 parameter regression model may only remove terms with rating variable R from the 24 parameter regression model in Section 3.1..1.1., thus, coefficients from the 15 parameter overnight regression model may be used and do the arithmetic calculation as:
C_Ooriginal=Reg1agy_Coef_tt * S_d +Reg1agy_Coef_dtt * P +Reg1agy_Coef_ttfq * S_d * S_z +Reg1agy_Coef_dttfq * P * S_z +Reg1agy_Coef_fq * S_z +Reg1agy_Coef_ttpos * I₁^S +Reg1agy_Coef_dttpos * I₁^P * If +Reg1agy_Coef_ttposfq * S_z * I₁^P +Reg1agy_Coef_dttposfq * S_z * I₁^P +Reg1agy_Coef_ttmat15 * S_d * YTM₁₅ +Reg1agy_Coef_ttposmat15 * I₁^S * YTM₁₅ +Reg1ag_Coef_ttfqmat15 * S_d * S_z * YTM₁₅ +Reg1agy_Coef_dttfqmat15 * P * S_z * YTM₁₅ +Reg1agy_Coef_ttposfqmat15 * I₁^S * S_z * YTM₁₅ +Reg1agy_Coef_dttposfqmat15 * I₁^P * S_z * YTM₁₅
4.6.4 Truncate Out-of-sample Transaction Cost

By using the same trade feature variables, calculate the truncation of out-of-sample predicted transaction costs by the following equation:
C_o=Sign(S_d+P) * max(0.05,min(2.5 * Reg1_Coef9_ttfq,Sign(S_d+P) * C_{O_original})), if ABS (S_d+P)=1
where Reg1_Coef9_ttfq is from the nine-parameter TC regression in Regression 1(Take regression of the first nine independent variables, and use the coefficient on Side * Size)
If ABS(S_d+P)≠1, truncation may not need to be performed to the out-of-sample transaction cost, C_o=C_{O_original}.
4.6.5 Blend the Cell Coefficients (Calculate tc)

For each bond, by using the maturity * credit cells, blend the truncated out-of-sample predicted transaction costs generated above with cell coefficients from Regression 3-5:
tc=C_O·(1+(BldReg3_Coef_spy3−1) * (0.8−0.3 * Max(0,Min(1,BldReg3_Se_spy3 * 100−100))))
C_O is from the above, Section 4.6.1.3.
BldReg3_Coef_spy3 and BldReg3_Se_spy3 are cell-average coefficient and standard error blended with Regression 3 Coefficient/Standard Error and the bond's cell weightings.
4.6.6 Calculate Final Transaction Cost Adjustment (Calculate tc3)

For each bond, use tc from the above times the issue-level multiplier to obtain the final transaction cost adjustment tc3:
tc₃=tc * (1+(Reg6_Coef_stc−1) * max(0,min(1,0.5−0.25 * 1n(8 * Reg6_Se_stc))))
tc is from the above, Section 4.6.1.4.
Reg6_Coef_stc and Reg6_Se_stc are coefficient and standard error from Regression 6

4.6.6.1. Assumption: Paired Clients Trades are dropped in real time

Paired clients trades are dropped as 2.3.2. defined as the following: an interdealer trade is identified as paired if it shares the same CUSIP, with execution time in the same second, and lot size with a client trade. Then client trades that are paired with interdealer trades are dropped, but the interdealer trade is retained.

4.6.6.2. Calculate Market Adjustment for the Trade

After calculated transaction cost adjustment has been calculated when a new trade occurs, market adjustment is calculated by using ETF price changes (ETF price differences between current ETFs and ETFs at last trade time).

4.6.7 Calculate Market Adjustments Using Betas from Regression 2

Market adjustments are calculated by using betas generated from overnight regression, i.e., β_l, β_h, β_m. Using these betas times the ETF price changes and sums them up as the following equation shows:
etf2(s,s−1)=β_l×(1n(LQD(s))−1n(LQD(s−1))) +β_h×(1n(HYG(s))−1n(LQD(s))−1n(HYG(s−1))+1n(LQD(s−1))) +β_m×(1n(TLT(s))−1n(IEI(s))−1n(TLT(s−1))+1n(IEI(s−1)))
where s is the time when new trade occurs, and s−1 is the time when last trade occurs.
4.6.8 For Agencies: Calculate Market Adjustments Using Betas from Regression 2

Similarly as Section 4.6.3.1. above, for agencies, only replace ETF tickers in the equation as:
etf2_agy(s, s−1)=β_a×(1n(AGZ(s))1n(AGZ(s−1))) +β_i×(1n(IEI(s))−1n(AGZ (s))−1n((s−1))+1n(AGZ(s−1))) +β_m×(1n(TLT(s))−1n(IEI(s))−1n(TLT(s−1))+1n(IEI(s−1)))
where s is the time the new trade occurs, and s−1 is the time the last trade occurs.
4.6.9 Calculate Issue-Level Market Adjustments

Market adjustments are adjusted by issue-level multiplier as:
etf23(s,s−1)=etf2(s,s−1) * (0.9 * (1+(Reg6_Coef_etf2(t)−1) * max(0, min(1,1−3 * Reg6_Se_etf2(t)))))
where t is the time when overnight regression runs, s is the time when new trade occurs, and s−1 is the time when last trade occurs etf2 is from the above, Section 4.6.3.1. Reg6_Coef_etf2,Reg6_Se_etf2 are coefficient and standard error from Regression 6

4.6.9.1. Update Value Estimation for the Trade

For a bond with trades at {s, s−1,s−2,s−3,s−4,s−5} during the 6 month window, tc3 and etf23 are generated as above to calculate transaction cost and market adjusted prices in value estimation process. Please see Section 3.6.2.2. for the definition of 6 month window in Regression 7.

In value estimation, all trades are reduced to the CUSIP*second level. In other words, the log differences in time below are set to seconds.

4.6.10 Collapse Multiple Trades at CUSIP*Second

As Section 4.2. shows, when new trades come in, multiple trades are collapsed at CUSIP*second level in the first step. This implies that there may be only one adjusted price for each CUSIP*second level. For each atomic trade, the adjusted price can be calculated as:
P_adj(s)=p(s)−tc3(s)
If multiple trades occurred in the same second, they may be collapsed in the same second into an average price. For example, assuming there are i trades occurred at the same second s, then the calculation of adjusted price at time s shown as above may be:

P adj ⁡ ( s ) = ln ⁡ ( lotisize ⁡ ( 1 ) $100 ) * ( p ⁡ ( 1 ) - tc ⁢ ⁢ 3 ⁢ ( 1 ) ) + ln ⁡ ( lotisize ⁡ ( 2 ) $100 ) * ( p ⁡ ( 2 ) - tc ⁢ ⁢ 3 ⁢ ( 2 ) ) + … + ln ⁡ ( lotisize ⁡ ( i ) $100 ) * ( p ⁡ ( i ) - tc ⁢ ⁢ 3 ⁢ ( i ) ) ln ⁡ ( lotisize ⁡ ( 1 ) $100 ) + ln ⁡ ( lotsize ⁡ ( 2 ) $100 ) + … + ln ⁡ ( lotsize ⁡ ( i ) $100 ) ( 4.2 )
4.6.11 Define Adjusted Price and Baseline Price

A baseline price is calculated as the simple average of transaction cost and market adjusted prices from the last 5 CUSIP*seconds with trades:

P ⁢ ⁢ 5 adj ⁢ ( s ) = P adj ⁡ ( s ) + P adj ⁡ ( s - 1 ) + P adj ⁡ ( s - 2 ) + P adj ⁡ ( s - 3 ) + P adj ⁡ ( s - 4 ) 5 , ( 4.3 )
where adjusted price P_adj(s) are obtained as Section 4.6.4.1. above. Adjusted price may be saved for all observed trades for the use of calculating a baseline price.
4.6.12 Define Price Difference X

Define a variable X as the difference between trade t′s transaction cost and market-adjust price and the baseline price. X is calculated as:
X=P_adj(s)−P5_adj(s−1)−MktA(s−5,s)   (4.4)
Where:
MktA(s=5,s)=etf23(s,s−1) +0.8 * etf23(s−1, s−2) +0.6 * etf23(s2, s3) +0.4 * etf23(s−3, s−4) +0.2 * etf23(s−4, s−5)   (4.5)
4.6.13 Calculate Estimated Value of Predicted Price Difference Y

Define a variable Y as the difference between trade t+1's transaction cost and market-adjusted price and the baseline price. Y is estimated by running Regression 7 on a set of independent variables. After a new trade occurs, using coefficients from overnight regression—Regression 7 multiplies related variables as the estimated value of Y (Note coefficients are saved from last night and held constant throughout each day, which is the same as other coefficients from Regression 1-6), denoted as

Y ^ = ∑ j = 1 9 ⁢ β ^ j × a j .
The detailed equation is as the following:
Ŷ=Reg7_Coef_x * X +Reg7_Coef_dx * X * I_d +Reg7_Coef_udx * X * U_d +Reg7_Coef_xLnft * X * T_d1 +Reg7_Coef_xLnt * X * T_d2 +Reg7_Coef_xig * X * IG_d +Reg7_Coef_xfq * X * T_s +Reg7_Coef_xsame * X * I +Reg7_Coef_xpos * X * Sum   (4.6)
where the independent variables in the above regression are defined as:

I d ⁢ - ⁢ Interdealer ⁢ ⁢ trade ⁢ ⁢ indicator ⁢ ⁢ variable = { 1 , if ⁢ ⁢ the ⁢ ⁢ trade ⁢ ⁢ is ⁢ ⁢ an ⁢ ⁢ interdealer ⁢ ⁢ trade 0 , otherwise ⁢ ⁢ U d ⁢ - ⁢ Unpaired ⁢ ⁢ interdealer ⁢ ⁢ trade ⁢ ⁢ indicator ⁢ ⁢ variable = { 1 , if ⁢ ⁢ the ⁢ ⁢ trade ⁢ ⁢ is ⁢ ⁢ an ⁢ ⁢ unpaired ⁢ ⁢ interdealer ⁢ ⁢ trade 0 , otherwise

• T_d1—Log differences in time between trade t+1 and t, defined in Stata code 1n(fs.dt/1000), this is defined on the CUSIP*second level, so the difference in time is measured in seconds; trade t+1 is the current time when new trade comes in, and trade t is the most recent trade before this new trade. (Note: execution time dt is measured in milliseconds (so fs.dt/1000 has the unit of seconds), and if they are not on the same trading day, appropriate rules of conversion may be applied, i.e., 1 day=24 * 60 * 60 seconds. According to an embodiment, this variable is coded as double Td1=log(T2−T1), where T2 and T1 are absolute trade execution times in seconds)

Note: Td1 is the log differences between next trade t+1 and the current trade t, except for the last row when (t+1) is current “calculation time” presented in the file as timestamp.

FIG. 6 depicts an exemplary timeline for when model price is triggered to be updated at some time T, and all the previous trades may be collapsed to CUSIP*seconds level to obtain the aggregated trades happened at t1, . . . , tN (tN<T).

First model price is available from the seventh trade at t7. So Td1 for t7 is defined as log(t8−t7), . . . Td1 for tN−1 is log(tN−tN−1). And for tN, Td1 is defined as log(T−tN), where T is the current “calculation time”. And this is defined as what the bond price would be if there was a trade at the current calculation time T. In addition, model price at T equals to model price tN+market adjustment from tN to T, i.e., 1n(ETF(T)−1nETF(tN)). For example, there is a trade occurred at 9:55:00, then model price gets updated at 9:55:01. At the evaluation time, say 10:00:00, the new model price may be the updated model price at 9:55:01 plus market adjustment between 9:55:01 and 10:00:00.

Implementation Note: Td1 is set to be zero for all trades including the last one, which may use the following formula:
Td1_t=1n((t+1)−t)=1n(1)=0(hardcoded to be 0) Td2 =1n(−s)

• T_d2−Log differences in time between trade t and t−1, defined in Stata code 1n(s.dt/1000), this is also defined on the CUSIP*second level, and the difference in time is measured in seconds; trade t is defined as the most recent trade before this new trade at current time, and trade t-1 is the last trade before the most recent trade

IG d ⁢ - ⁢ Investment ⁢ ⁢ Grade ⁢ ⁢ indicator ⁢ ⁢ variable = { 1 , if ⁢ ⁢ the ⁢ ⁢ trade ⁢ ⁢ is ⁢ ⁢ an ⁢ ⁢ investmetn ⁢ ⁢ grade ⁢ ⁢ trade 0 , otherwise

• T_s—Average trade size (Aggregated lotsize). This is defined and calculated as

T s = ∑ w i n ,
where n equals the number of trades occurred in the same CUSIP*second, and

w = ln ⁡ ( lotsize 100 ) , and ⁢ ⁢ w = ln ⁡ ( lotsize 100 ) + ln ⁡ ( 2 ) ⁢ ⁢ if ⁢ ⁢ lotsize = 5000000 ⁢ ⁢ or ⁢ ⁢ lotsize = 1000000 ,
and MAquantityindicator=“E” (this is defined in Section 2.5., MAquantityindicator indicates if the reported TRACE quantity is truncated, and “E” for estimated if truncated) Note: lotsize may be truncated at $5M and $1M, and weighted it as if it really was twice that size. The Stata code for this process is:
/* Log linear weight with a bonus for truncated values */

• • gen w=1n(lotsize/100)
  • replace w=w+1n(2) if
    (lotsize==500000|lotsize==1000000)&MAquantityindicator==“E” drop MAquantityindicator
    So if a lotsize is at $5M or $1M with a “E” as estimated if truncated, the weight formula as w=w +1n(2) is used.
    The weights in MP1 and MP2 may use the similar weight calculation in all CUSP*second averaging.

I ⁢ - ⁢ Indicator ⁢ ⁢ variable ⁢ ⁢ for ⁢ ⁢ trade ⁢ ⁢ t ⁢ ⁢ and ⁢ ⁢ t - ⁢ 1 ⁢ ⁢ occurring ⁢ ⁢ on ⁢ ⁢ the ⁢ ⁢ same ⁢ ⁢ calendar ⁢ ⁢ day = { 1 , if ⁢ ⁢ trade ⁢ ⁢ t ⁢ ⁢ and ⁢ ⁢ t - 1 ⁢ ⁢ occurring ⁢ ⁢ on ⁢ ⁢ the ⁢ ⁢ same ⁢ ⁢ calendar ⁢ ⁢ day 0 , otherwise

• Sum−Sum of Side and Paired=S_d+P=tt+dtt
  Calculate Predicted Price

Now, since the estimated value Y was calculated in previous section 4.6.4.4., the predicted price can be obtained:
PredPrice(s)P5_adj(s, s−1)+MktA(s−5s)+Ŷ  (4.7)
Where:
MktA(s5,s)=etf23(s, s−1) +0.8 * etf23(s−1, s−2) +0.6 * etf23(s−2, s−3) +0.4 * etf23(s−3, s−4) +0.2 * etf23(s−4, s−5)
Note: For Y only, trades that are eventually cancelled or replaced are not considered.
4.6.14 Calculate New Price Difference X₂ and New Predicted Price

Construct a new baseline price and average the predicted next-trade price as the following:
X₂=PredPrice(s)−PredPrice(s−1), predicted price PredPrice(s) is obtained from the above, Section 4.6.4.3.   (4.8)

Then this new price difference X₂, and the coefficients from overnight regression are used in Regression 7 to generate a new estimated value of Y, denoted as Ŷ₂. The detailed equation is as the following:
Ŷ₂=Reg72Coef_x2 * X₂ +Reg72_Coef_x2ud * X_{2 *} U_d +Reg72_ x2Lnft * X_{2 *} T_d1 +Reg72_Coef_x2Lnt * X₂ * T_d2 +Reg72_Coef_x2ig * X₂ * IG_d +Reg72_Coef_x2fq * X_{2 *} T_s +Reg72_Coef_x2pos * X₂* Sum   (4.9)
where the independent variables in the above regression are defined as:

U d ⁢ - ⁢ Unpaired ⁢ ⁢ interdealer ⁢ ⁢ trade ⁢ ⁢ indicator ⁢ ⁢ variable = { 1 , if ⁢ ⁢ the ⁢ ⁢ trade ⁢ ⁢ is ⁢ ⁢ an ⁢ ⁢ unpaired ⁢ ⁢ interdealer ⁢ ⁢ trade 0 , otherwise

• T_d1—Log differences in time between trade t+1 and t, defined in Stata code 1n(fs.dt/1000)
• T_d2—Log differences in time between trade t and t−1, defined in Stata code 1n(s.dt/1000)

IG d ⁢ - ⁢ Investment ⁢ ⁢ Grade ⁢ ⁢ indicator ⁢ ⁢ variable = { 1 , if ⁢ ⁢ the ⁢ ⁢ trade ⁢ ⁢ is ⁢ ⁢ an ⁢ ⁢ investmetn ⁢ ⁢ grade ⁢ ⁢ trade 0 , otherwise

• T_s—Average trade size
• Sum−Sum of Side and Paired=S_d +P=tt +dtt

A new predicted price, denoted as PredPrice2(s) is obtained in the following:
PredPrice2(s)=PredPrice(s−1)+etf23(s−1,s)Ŷ₂(s)   (4.10)
4.6.15 Calculate Model Mid Price

Model Mid price equals to the average of the predicted next-trade price. A 50-50 ratio is used out-of-sample as a measure of current value for prediction of as the formulae shows:
Model Mid Price=0.5 * PredPrice(s)+0.5 * PredPrice2(s)   (4.11)
4.6.16 Calculate Model Bid Price
Model Bid Price=Model Mid Price+ldb3 (ldb3<0)   (4.12)
ldb and ldb2 have calculated in previous section, Section 4.4.. In (4.12), and Idb3=max(−0.26,min(−0.035,ldb)). ldb3 is used in Model Bid Price calculation. 4.6.17 Calculate Model Ask Price
Model Ask Price=2 * Model Mid Price—Model Bid Price   (4.13)

• • 4.7 Update in Response to ETF Price Changes

Another trigger for updating the value estimation in model pricing is ETF price changes. In an exemplary embodiment, ETF data sampled every 15 minutes or more frequent by tick may be used during regular equity trading hours (this may be configurable). If no new trade occurred, but only ETF price differs between different time stamps when the ETF prices are checked, only market adjustment is required to update in this case, i.e., use the same transaction cost adjustment from the most recent trade to update the value estimation in model pricing. In an embodiment, ETF data sample time every 15 minutes may be used, this may be switched to every 5 minutes. As frequent as practical may be used for the production version. In Omega, ETF price may be sampled every 15 minutes. In addition, this quantity is calculated whenever a new trade is observed. To differentiate it from the model bid/mid price generated in Section 4.6. above, where model prices are triggered by new trades, it may be denoted as Model Pred Bid/Mid Price. This may be used in Model Pricing Phase Two as well as in back testing. To do so, view the trade time as a new ETF price change time, denoted as s below.

4.7.1.1. ETF Price Time Window

If the ETF price corresponding to trade time s is not available, use the following default rules to decide which ETF may be used, as also discussed in Section 2, Input Data Preparation:

• For the time range of ETFs, the previous ETF may be used, regardless of how far it is. So if there is a trade at 3 am, the most recent ETF closing price may be used. If bond market was open but stock market was closed, the most recent close price, which maybe 1 day or 1.5 day ago, may be used.
• For Fair Value, opening price may be avoided. In an exemplary embodiment, use 9:30 snap (which may be the open or may be a few second later) and this may be a better predictor of future prices than the local close. It may be that for bond trades occurring right around 9:30, it is better to append the 9:35 ETF prices.
• In an exemplary embodiment, the ETF suspect prices may be excluded, instead the ETF price 5 minutes before (or the most recent one) may be used.

4.7.1.2. Calculate Market Adjustments Using Betas from Regression 2

This follows the same steps in Section 4.6.3.1.-4.6.3.3., using ETF price changes to calculate market adjustments. Market adjustments are calculated by using betas generated from overnight regression—Regression 2 and blended with issue-level betas. Using these betas times the ETF price changes and sums them up as the following equation shows:
etf2(s,s−1)=β_l×(1n(LQD(s))−1n(LQD(s−1))) +β_h×(1n(HYG(s))1n(LQD(s))1n(HYG(s−1))+1n(LQD (s−1))) +β_m×(1n(TLT(s))−1n(IEI(s))−1n(TLT(s−1))+1n(IEI(s−1)))
where s is the time when the new ETF prices are checked which triggers the model to update,
while s−1 is the last time ETF prices were checked.

4.7.1.3. For Agencies: Calculate Market Adjustments Using Betas from Regression 2

For agencies, only replace ETF tickers in the above equation as:
etf2_agy(s,s−1)=β_a×(1n(AGZ(s))−1n(AGZ(s−1))) +β_i×(1n(IEI(s))−1n(AGZ(s))−1n(IEI(s−1))+1n(AGZ(s−1))) +β_m×(1n(TLT(s))−1n(IEI(s))31 1n(TLT(s−1))+1n(IEI(s−1)))
where s is the time when the new ETF prices were checked, which triggers the model to update, while s−1 is the last time ETF prices were checked.

4.7.1.4. Update Value Estimation for ETF Price Change

If the model is updated by ETF price changes, only market adjustments may be added that have been calculated above to model mid price (obtained and saved from Section 4.6.) of the most recent trade as:
Model Pred Bid Price(s)=Model Bid Price(t)+etf2(s,t) =Model Bid Price(t)+beta * (lnETF(s)−lnETF(t))   (4.14)
Model Pred Mid Price(s)=Model Mid Price(t)+etf2(s,t) =Model Mid Price(t)+beta * (lnETF(s)−lnETF(t))   (4.15)
where s is the time when we check the new ETF prices, and t is the most recent value estimation. etf2 is calculated by using three betas and its matched ETF prices, shown as in Section 4.6.3.

• • 4.8 An Example of Time Series in Value Estimation

When value estimation is updated by new trades or ETF price changes at real time, calculate the log time difference between current time (t+1) and the most recent trade time (t). When running regressions using historical data, the log time difference can be defined as the next trade time (t+1) and the most recent trade time (t), since the next trade time (t+1) in the history data is known. For example, for real-time calculation, if the most recent trade was at 10:00:00 and it is now 10:00:01, the log may be set to a difference between t+1 and t as log(1) in this case. If the model at 10:00:03 is updated, it may be changed to log(3). And so on.

• • 4.9 Reconstruct the Value Estimate for Cancelled/Replaced Trades

After a cancellation or replacement as stated in 2.3.3., the value estimate may be reconstructed without the cancelled trade or with the new data for the replaced trade (trades are sorted using execution time). This requires going back to the last trade before the cancelled/replaced trade, and then recalculating the value estimates.

5. GUI Design and Functionality

• • 5.1 Model Top Menu

FIG. 7 depicts an exemplary menu. From the top menu of Omega, the user can choose Eval and then find US Model Pricing. Under Model Pricing, there are four submenus priced separately: agencies, investment grade, and high yield bonds; also, Model Pricing Configurations (sectors can be chosen on configuration screens). More options may be added to the sub-menu under each category at Phase Two, for example, Notifications, Inbox, Confidence Interval (Quality Checks), if necessary.

• • 5.2 Worksheet Enhancements

In Worksheet Enhancements, new fields are added into the existing bond-level worksheet under Sector in IG and HY or Ticker in Agencies. This may be applied to real-time pricing and 3PM/4PM snap pricing.

New Fields: Model Bid/Mid Spread, Model Bid Price, Model Mid Price, Model/Eval Diff,

New fields in the screen are defined by the fields in the table below:

		Model Variable
Field	GUI Name	Name	Data Range	Example
Model	Model Bid
Bid/Mid	Spread
Spread	Model Mid
	Spread
Model Bid	Model Bid	Model Bid Price	Positive floating
Price	Price	= Model Mid	number
		Price + ldb (or
		ldb2 or ldb3), ldb
		is the large dealer
		buy transaction
		cost estimated by
		the model (ldb2 is
		the large dealer
		buy transaction
		cost predicted
		from the TC
		model with the
		issue-level
		multiplier, and
		ldb3 = min (0,
		ldb2)
Model Mid	Model Mid	Model Mid Price	Positive floating
Price	Price	= 0.5	number
		* PredPrice(s)
		+ 0.5
		* PredPrice2(s)
Model/Eval	Model/Eval	This is the
Diff	Diff	difference
		between Model
		Mid Price and
		Evaluation Mid
		Price
Model 3PM	Model 3PM
Bid/Mid Price	Bid Price,
	Model 3PM
	Mid Price,
Model 4PM	Model 4PM
Bid/Mid Price	Bid Price,
	Model 4PM
	Mid Price,
Model	Model 3PM
3PM/4PM	Bid Spread
Bid/Mid	Model 3PM
Spread	Mid Spread
	Model 4PM
	Bid Spread
	Model 4PM
	Mid Spread

Note: Model 3 PM/4 PM price/spread is the model price/spread under the mode 3 PM or 4 PM. The model price may be copied at 3 pm and 4 pm to this field. No evaluator action is required for this.

5.2.1.1. IG/HY Worksheet Enhancements

FIG. 8 depicts an exemplary Investment Grade Worksheet Enhancements screen and a High Yield Worksheet Enhancements screen, which are the same.

5.2.1.2. Agency Worksheet Enhancements

FIG. 9 depicts an Agency Worksheet screen. Similarly as USIG Worksheet, new fields in Section 5.2. are added onto Agency Worksheet screen. There are three modes on Dashboard: Real Time, 3 PM, and 4 PM. In each mode, there are one set of fields to show model price:

• Model (3 PM or 4 PM) Bid/Mid Spread
• Model (3 PM or 4 PM) Bid/Mid Price
• Model/Eval Diff
  • 5.3 Trade Data Enhancements

In Trade Data Enhancements, new fields are added into the existing trade-level grids for each security in IG and HY or each Identifier in Agencies. This is applied to real-time pricing (3 pm/4 pm snap pricing is acceptable but not required). New Fields: Model Side Indicator, Model Paired Indicator, Model Paired, Model Trade-to-trade Change in Price Ap, Model Updated Time, Model Bid/Mid/Ask Price, Model Observation Weights, Model Out-of-sample TC, Model Truncated Out-of-sample TC, Model Rescaled TC, Model Final TC

New fields in the screen are defined by the fields in the table below:

		Model Variable	Data
Field	GUI Name	Name	Range	Example
Model Side	Model Side	I1S (Sd)	0 or 1	1
Indicator	Indicator
Model Paired	Model Paired	I1P (P)	0 or 1	0
Indicator	Indicator
Model Paired	Model Paired	P	−1, 0 or 1	−1
Reported Time	Trade	dt_report	Date and	11/10/
	Reported		time	2008
	Time		(mm/dd/	14:46:00
			yyyy
			hh:mm:ss)
Model	Mdl.	w (calculation	Positive	4.86E−05
Observation	Observation	is defined in	floating
Weights	Weights	Section 2.4.3.)	number
		Note: this is
		weight
		adjustments
		defined in
		Table 5
Model Out-of-	Mdl. Out-of-	CO_original
sample TC	sample TC
Model	Mdl.	CO
Truncated	Truncated
Out-of-sample	Out-of-sample
TC	TC
Model Rescaled	Mdl. Rescaled	tc	Floating	0.644615
TC	TC		number
Model Final TC	Mdl. Final TC	tc3	Floating	0.666422
			number

When collapsing trade level data to CUSIP*second, atomic trade level data may be published in the above fields. Trades occurred in the same second may share the same executed time (or reported time), and the same transaction costs as used in aggregated values in the calculation of transaction costs. However, they may show their individual Side Indicator, Paired

Indicator, Weights, etc.

5.3.1.1. IG/HY Trade Data Enhancements

FIG. 10 depicts exemplary Investment Grade and High Yield screens, which have the same Trade Data Enhancements screen.

5.3.1.2. Agency Trade Data Enhancements

FIG. 11 depicts an exemplary trade data enhancement screen.

• • 5.4 Model Pricing Configurations

Configuration screens described herein work under the whole model.

5.4.1.1. Data Preparation

FIG. 12 depicts an exemplary model pricing configuration screen for data preparation. On the top of the screen, sectors can be switched between: Corp (which includes IG and HY), and Agencies (shown as AGY in the dropdown box).

5.4.1.2. Transaction Cost Adjustment

FIG. 13 depicts an exemplary model pricing configuration screen for transaction cost adjustment. Similarly, on the top of the screen, sectors can be switched between: Corp (which includes IG and HY), and Agencies (shown as AGY in the dropdown box).

5.4.1.3. Market Adjustment

FIGS. 14 and 15 depict exemplary model pricing configuration screens for market adjustment. The tab of market adjustment configurations are applied to each of the three pricing methods, i.e., IG, HY and Agency. On the top of the screen, sectors can be switched between: Corp (which includes IG and HY), and Agencies (shown as AGY in the dropdown box).

6. Output Files

The output files in this section provide data analysis for Model Pricing, especially supporting Methodology to check the performance of the model. At 10 am, 12 pm, 3 pm and 4 pm each day, it may publish out two files (in Excel.csv format): one is the bond-level output file, and the other is the trade-level output file.

• • 6.1 Bond-Level Output File

The bond-level output file may contain all the statistics data for each certain security: Model Price (Bid/Mid/Ask Price), New Price (Bid/Mid/Ask Price), Difference in Prices, Last 5 Trades' Price, Last 5 Transaction Cost Adjustments, Transaction Cost Coefficients, Market Adjustment Coefficients, Value Estimate Coefficients. This file includes all the regression results generated while running the model. Table 8 shows all the available fields in the bond-level output file.

TABLE 8
Available Fields of Bond-level Output File
Available Fields

Sector	Security ID	Security Description
Model Bid Price	Model Mid Price	Model Ask Price
New Bid Price	New Mid Price	New Ask Price
Diff in Bid Price	Diff in Mid Price	Diff in Ask Price
Last Trade Price	Last Second Trade Price	Last Third Trade Price
Last Fourth Trade Price	Last Fifth Trade Price	Last Transaction Cost Adj
Last Second Transaction	Last Third Transaction Cost Adj	Last Fourth Transaction Cost
Cost Adj		Adj
Last Fifth Transaction Cost	Reg1_Coef_tt	Reg1_Coef_dtt
Adj
Reg1_Coef_ttfq	Reg1_Coef_dttfq	Reg1_Coef_fq
Reg1_Coef_ttpos	Reg1_Coef_dttpos	Reg1_Coef_ttposfq
Reg1_Coef_dttposfq	Reg1_Coef_ttrat	Reg1_Coef_ttmat15
Reg1_Coef_ttposrat	Reg1_Coef_ttposmat15	Reg1_Coef_ttfqrat
Reg1_Coef_ttfqmat15	Reg1_Coef_ttfqmat15rat	Reg1_Coef_dttfqrat
Reg1_Coef_dttfqmat15	Reg1_Coef_dttfqmat15rat	Reg1_Coef_ttposfqrat
Reg1_Coef_ttposfqmat15	Reg1_Coef_ttposfqmat15rat	Reg1_Coef_dttposfqrat
Reg1_Coef_ ttposfqmat15	Reg2_Coef_sLQD	Reg2_Coef_sLQDmat10
Reg2_Coef_sLQDrat	Reg2_Coef_sLQDmat10rat	Reg2_Coef_sLQDhy
Reg2_Coef_sLQDhyrat	Reg2_Coef_sLQDmat10hy	Reg2_Coef_sLQDmat10hyrat
Reg2_Coef_sHL	Reg2_Coef_sHLmat10	Reg2_Coef_sHLrat
Reg2_Coef_sHLmat10rat	Reg2_Coef_sHLhy	Reg2_Coef_sHLhyrat
Reg2_Coef_sHLmat10hy	Reg2_Coef_sHLmat10hyrat	Reg2_Coef_sLM10a
Reg3_Coef_spy3	Reg3_Se_spy3	Reg4_Coef_col
Reg4_Se_sel	Reg5_Coef_coh	Reg5_Se_seh
Reg6_Coef_stc	Reg6_Se_stc	Reg6_Coef_etf2
Reg6_Se_etf2	Reg7_Coef_x	Reg7_Coef_dx
Reg7_Coef_udx	Reg7_Coef_xLnft	Reg7_Coef_xLnt
Reg7_Coef_xig	Reg7_Coef_xfq	Reg7_Coef_xsame
Reg7_Coef_xpos	Reg72_Coef_x2	Reg72_Coef_x2ud
Reg72_Coef_x2Lnft	Reg72_Coef_x2Lnt	Reg72_Coef_x2ig
Reg72_Coef_x2fq	Reg72_Coef_x2pos	Years-To-Maturity
Last Trade Adjusted Price	Last Second Trade Adjusted	Last Third Trade Adjusted
Padj1	Price Padj2	Price Padj3
Last Fourth Trade Adjusted	Last Fifth Trade Adjusted Price	Last 5 Average TCMA Price
Price Padj4	Padj5	P5adj
X	X2	PredPrice
PredPrice2

Last Trade Price is the most recent aggregated trade price, i.e., if there are multiple trade occurred in one second, Last Trade Price may display the weight-averaged aggregation of all trades in that 1 second. Years-To-Maturity may be calculated based on the most recent trade. In addition, all the coefficients from overnight regressions keep the same for each day.

• • 6.2 Trade-Level Output File

Each trade-level output file may include all the trades' data processed by the model in one day by the published time, and fields in this file are the same as columns shown in Trade Data Enhancements for IG/HY and Agencies, respectively. Table 9 shows all the available fields in the trade-level output file:

TABLE 9
Available Fields of Trade-level Output File
Available Fields

Side	Size	Trade Spread
Trade BM	Trade Time	Time Applied
Model Side Indicator	Model Paired Indicator	Matched Trade ID
Model Updated Time	Trade Yield	Trade Price
LQD Price	HYG Price	TLT Price
IEI Price	Model Paired

7. Data Dependencies

TRACE data with the reporting party side variable is available back to November, 2008, and for agencies available from 2010, and these are the dates when the data start. To count the maximum years' of historical data estimates are used by working backwards through the code as the following:

• An estimate of pprice2 for July 2013 use estimates of pprice from January 2013 to June 2013 (this is the second value estimation step).
• Estimates of pprice from January 2013 use estimates of transaction costs (tc3 and etf23) from July 2012 to December 2012 (this is the first value estimation step).
• Estimates of tc3 and etf23 from July 2012 use estimates of tc and etf2 from July 2010 to July 2012 (this is the issue-level TC and MA multiplier step).
• Estimates of tc and etf2 from July 2010 could use py3 from July 2008 to July 2010 (this is the issue-level TC and MA step).
• An estimate of py3 from July 2008 could have used data from July 2006 to July 2008 (this is the market-wide TC step).

The above shows that if an estimation of everything with the maximum possible data is desired, 7 years of data, which will be available in early 2016, is needed. However, the minimum requirement on the length of historical data required for real time model is 3 years (including calculation of transaction cost from Regression 1) in order to generate all regression coefficients. But the more data we have, the better quality the model has. So Omega may be programmed to discard data that is 7+ years old.

• • 7.1 Reference Data

Bond reference data for investment grade and high yield bonds may be required, including the bond attributes of maturity date, currency, the flag of TRACE eligible data, etc. Also, it may identify that the bond is not convertibles, convertible preferreds, preferreds, or index-linked notes.

• • 7.2 TRACE Trade History

The TRACE trades data with 3 years history may be available in Omega as the rolling window of the regressions in Section 3.

• • 7.3 Real-time TRACE trade feed

During the day, the real-time TRACE trade feed may also be available in Omega for the real-time value estimation process.

• • 7.4 ETF Price History

Also, three-year daily ETF prices in real-time ticking may be available, and the tickers that are used in the model are LQD, HYG, IEI, and TLT.

• • 7.5 ETF Price Real-Time Ticking Feeds

During the day, the real-time ticking feeds for the above four ETFs may also be needed in Omega for real-time value estimation process.

• • 7.6 Data Migration

As stated herein, this length of historical data may be sufficient to run the model and generate all regression coefficients.

8. Configurations

The following table shows what is configured at model level:

	Description/Functions with configurable	Data
Name	parameters	Object	Section	Default
Minimum	The minimum number of trades for a bond to	Integer	1.2.	6
Trades for	calculate the averages in the model	at least
A Bond		equals
		to 6
Weights Adjustment	Function (2.2) Adjusted ⁢ ⁢ Weights = Weight 0.8 + 0.3 * S Z * ( 1 - ABS ⁡ ( S d + P ) 2 ) + 0.25 * ABS ⁢ ( S d ) - 0.15 * ( S d + P )		2.4.3.	0.8, 0.3, 0.25, 0.15
Truncated	Functions (3.3) and (3.4)		3.1.1.3.	0.05,
In-sample	Co(t + 1) = Sign(Sd(t + 1) + P(t + 1)) *			2.5
and Out-of-	max(0.05, min(2.5 * coef (t),Sign(Sd(t + 1) +
sample	P(t + 1)) * CO_original(t + 1))) , if ABS (Sd(t +
Predicted	1) + P(t + 1)) = 1
Transaction	CI(t + 1) = Sign(Sd(t + 1) + P(t + 1)) *
Costs	max(0.05, min(2.5 * coef(t), Sign(Sd(t + 1) +
	P(t + 1)) * CI_original(t + 1))), if ABS(Sd(t +
	1) + P(t + 1)) = 1
Rescaled	Function (3.18)		3.4.3.	0.8, 0.3
Transaction	tc =
Cost	CO · (1 + (β1p− 1) *
	(0.8 − 0.3 * Max (0, Min(1, Ēp* 100 − 100))))
New LQD	Function (3.19)		3.4.4.1.	5, 0.4
Beta	βl = Max(5, βLQD * 0.4 + β1l * 0.4)
New HYG-	Function (3.21)		3.4.4.2.	0.8,
LQD Beta	βh = βHYG-LQD * 0.8 + 0.8 * (β1h = βHYG-LQD) *			0.2, 4
	(1 − 0.2 * max (0, min (4, Ēh)))
Final	Function (3.28)		3.5.2.	0.5,
Transaction	tc3 =			0.2, 8
Cost	tc * (1 + (  − 1) * max(0, min(1, 0.5 − 0.25 *
Adjustment	ln (8 * Ēp))))
Final Market Adjustment	Function (3.29) etf ⁢ ⁢ 23 = eft ⁢ ⁢ 2 * ( 0.9 * ( 1 + ( - 1 ) * ⁢ max ⁡ ( 0 , min ⁡ ( 1 , 1 - 3 * σ 2 ⁡ ( ) ) ) ) )		3.5.3.	0.9, 3

9. Notifications

No notifications may be required for Phase One. Once the confidence measure is implemented in Phase Two, notifications may be performed.

10. Appendix A: Ratings Mapping Between Agencies and IDC Bucket

IDC Ratings		S&P
Bucket	S&P	Numerical	intSP	R (rat)	Moody's	Fitch	Description

AA or Higher	AAA	20	6	0	Aaa	AAA	Prime
AA or Higher	AA+	19	6	0	Aa1	AA+	High grade
AA or Higher	AA	18	6	0.0625	Aa2	AA
AA or Higher	AA-	17	6	0.125	Aa3	AA−
A	A+	16	5	0.1875	A1	A+	Upper
A	A	15	5	0.25	A2	A	medium
A	A−	14	5	0.3125	A3	A−	grade
BBB	BBB+	13	4	0.375	Baa1	BBB+	Lower
BBB	BBB	12	4	0.4375	Baa2	BBB	medium
BBB	BBB−	11	4	0.5	Baa3	BBB−	grade
BB	BB+	10	3	0.5625	Ba1	BB+	Non-
BB	BB	9	3	0.625	Ba2	BB	investment
BB	BB−	8	3	0.6875	Ba3	BB−	grade
							speculative
B	B+	7	2	0.75	B1	B+	Highly
B	B	6	2	0.8125	B2	B	speculative
B	B−	5	2	0.875	B3	B−
CCC or Lower	CCC+	4	1	0.9375	Caa1	CCC	Substantial
							risks
CCC or Lower	CCC	3	1	1	Caa2		Extremely
							speculative
CCC or Lower	CCC−	2	1	1	Caa3		In default
CCC or Lower	CC	1	1	1	Ca		with little
CCC or Lower	C	0	1	1			prospect for
							recovery
CCC or Lower	D	−12	1	1	C	DDD	In default
NR		0	1	1			Not rated

In an exemplary embodiment, if there are 2 or more ratings that do not map into the same bucket, take the median rating if all 3 ratings from the rating agencies are present; and if there are ratings from 2 rating agencies, use the rule S&P>Moodys>Fitch to predict transaction costs in this model. For Fitch's CCC, use numerical value 4, and for Moody's Ca use numerical value 1, which means the higher numerical rating is used for ratings that have more than one numerical values.

For unrated bonds, currently they are getting SPrat=0. However, in an exemplary embodiment, an approximate rating may be calculated from the spread to Treasures, on a fairly infrequent basis, e.g. once a month or so. If there are no ratings, the user may choose from the issue's yields. In an exemplary embodiment, with no ratings the user could infer a rating from the spread to Treasures. Each day the user could calculate, for example, a kernel smoothed median rating as a function of yield spreads, created cutoffs, and classify the unrated bonds accordingly.

11. Appendix B: Getting TRACE Data

This section provides how the user obtains TRACE data as a reference, however, it is not required. The user may merge two files to get TRACE data—one that includes all variables disseminated by TRACE and use the name “Fat TRACE” for this file, and one that includes additional variables created by MarketAxess, and this is called as “Skinny”. Variables are created and used as the follows from the files in the parenthesis:

• IssuepriceID (Both)
• Sequencenumber (Both)
• Cusip (Skinny) and InstrumentCusip (Fat)
• Report Date and Time (Fat) and FirstReportTime (Skinny)
• Effective Date and Time (Fat) and TransactionTime (Skinny)
• TradeAction (Skinny) and CancelFlag and CorrectionFlag (Fat)
• Price (Both)
• Reporting Party Side (Skinny) and Trade_Type (Fat)
• Quantity (Fat) and Lotsize (Skinny)
• Is_Suspect (Both)
• SpecialPrice (Fat)
• QuantityIndicator (Fat)
• SalesCondCode (Fat)
• SecondModifier (Fat)
• AsOfFlag (Both)
• CommissionFlag (Fat)
• W1Flag (Fat)

12. Appendix C: Variable Dictionary

Variables in GCAT files

price	double	%9.0 g	Price in points (par = 100)
lotsize	long	%12.0 g	lotsize in $
spread	double	%8.0 g	Spread to treasuries as calculated by Market Axess
			(not used)
yield	double	%9.0 g	Yield as calculated by Market Axess (not used)
dt	double	% tc	Execution Date-Time variable (in Stata, milliseconds
			since Jan. 1, 1960, but should be outputted in
			CSYs in a textual format)
cusip	str8	%9 s	8-digit CUSIP
piid	long	%12.0 g	Categorical variable: aggregated a few cases of CUSIP
			or instrumentID changes into a common identifier
ytm	float	%9.0 g	Years to Maturity from c
yld	float	%9.0 g	Not used
sprat	str4	%9 s	S&P credit rating (or rating estimated from
			Moodys/Fitch rating) in text
SPrat	byte	%8.0 g	Numerical version of S&P rating (AAA = 20,
			AA+ = 19, BB+ = 10, CCC+ = 4,
			CCC = 3, CC = 0, D = −12
bigsubset	str4	%9 s	Aggregation of the subset variable provided by
			IDC (not used)
InHYG	float	%9.0 g	Most recent In(HYG total return index) as of
			execution time
InIEF	float	%9.0 g	Most recent In(IEF total return index) as of
			execution time
InIEI	float	%9.0 g	Most recent In(IEI total return index) as of
			execution time
InLQD	float	%9.0 g	Most recent In(LQD total return index) as of
			execution time
InTLT	float	%9.0 g	Most recent In(TLT total return index) as of
			execution time
n1	float	%9.0 g	Numbers trades within values of PIIDA, in order of
			execution time (with ties broken by values of n)
yrmo	long	%8.0 g	Year month variable (January 2009 = 200901)
benchiagt	float	%9.0 g	Not used
tt	float	%9.0 g	=+1 for dealer sells; −1 for dealer buys; 0 for
			interdealer
dtt	byte	%8.0 g	=0 for client trades and unpaired interdealer trades;
			+1 for ID trades paired with dealer sell; −1 for paired
			with dealer buy (paired = same CUSIP, second,
			lotsize)
fq	float	%9.0 g	Truncated log-linear function of lotsize
			(=0 for <=$50k, =1 for >=$1M, log-linear
			in between)
ttfq	Float	%9.0 g	TT*FQ
dttfq	float	%9.0 g	DTT*FQ
by	float	%9.0 g	Not used
spr	float	%9.0 g	Not used
n	long	%12.0 g	Trade identifier (created by me; used for disassembling
			and reassembling datasets)
a	float	%9.0 g	=1 If ultimately cancelled
piida	float	%9.0 g	Grouping of combinations of PIID and A (in TC
			model, all A = 1 observations are dropped, so this
			maps one-to-one to PIID)
m	float	%9.0 g	1 to N numbering of months appearing in data
			(November 2008 = 1, January 2012 = 44)

Variables in TPBED5 files

price	double	%9.0 g	As above
dt	double	%tc	As above
cusip	str8	%9 s	As above
piid	long	%12.0 g	As above
ytm	float	%9.0 g	As above
SPrat	byte	%8.0 g	As above
InHYG	float	%9.0 g	As above
InIEF	float	%9.0 g	As above
inIEI	float	%9.0 g	As above
inLQD	float	%9.0 g	As above
inTLT	float	%9.0 g	As above
n1	float	%9.0 g	As above
tt	byte	%9.0 g	As above
dtt	byte	%8.0 g	As above
fq	float	%9.0 g	As above
n	long	%12.0 g	As above
a	byte	%9.0 g	As above
piida	int	%9.0 g	As above
betam	float	%9.0 g	Beta estimated for TLT-IEI factor
tc	float	%9.0 g	Trading cost estimated from weighted average of
			market-level and cell-level models
betal	float	%9.0 g	Beta estimated for LQD factor
betah	float	%9.0 g	Beta estimated for HYG-LQD factor
etf2	float	%9.0 g	Market adjustment from last trade calculated using
			betam, betah, betal
yq	float	%9.0 g	A variable that groups months in the data
			(November 2008 = 107, June 2012 = 150)
w	float	%9.0 g	Weight used in regressions
p	float	%9.0 g	Counter of unique values of PIID (also used as
			a counter of unique values of gcat
			(credit* maturity ceil) earlier in code)
copi	float	%9.0 g	Issue-level transaction cost coefficient
sepi	float	%9.0 g	Issue-level transaction cost standard error
coe	float	%9.0 g	Issue-level market adjustment coefficient
see	float	%9.0 g	Issue-level market adjustment standard error
tc3	float	%9.0 g	Trading cost estimated from TC and COPI
emult	float	%9.0 g	Market adjustment multiplier estimated from COE
etf23	float	%9.0 g	ETF2*EMULT

Other important variables

TTPOS			=1 if dealer sell
DTTPOS			=1 if paired with dealer sell
TTPOSFQ			TIPOS*FQ
DTTPOSFQ			DTTPOS*FQ
PY0			Out of sample predicted transaction cost from 9
			parameter market-level model
PY3			Out of sample predicted transaction cost from 24
			parameter market-level model
PY3b			Partly in-sample predicted transaction cost from 24
			parameter market-level model
The other variables should be obvious from the code (e.g., interaction terms), but feel free to ask any questions

13. Appendix D: Regression Framework and Formulae

In this Appendix regression framework is described in general and regression formulae applied to TC model and Market Adjustment in specific. Note that all regressions involved may be weighted regressions. Also note that the design matrix and the right-hand-side of regressions include 1^st differences, except for the constant term in design matrix.

13.1 Assumptions and General Settings

A few assumptions as basis of framework are made and describe general settings for TC model and Market Adjustment applications. Regressions are run in rolling windows. The generic form of a rolling window is [t−24,t] with t being a time unit in month. Observations come with execution times {t_i}. The execution times are also used to calculate 1^st differences. Let p_t denote the price at execution time t. Then the 1^st difference for price is calculated according to the follows:
p_ti−p_ti−1=Δp_iϵΔp⇔t_i−1<t_i;t_i,t_i−1ϵ[t−24,t];(t_t−1, t_i)∩[t−24,t]=0    (12.1)
(t_i−1, t_i)∩[t−24,t]=0 means there is no execution between t_i−1 and t_i, 1^st differences for other quantities are also calculated according to rules above. The 1^st difference calculations are based on grouping according to certain id's.

• • 13.2 Regression Formulae and Components

The following notations are defined:

Let f_j(t_i, . . . ) be the j^th basis function at time t_i.

Let q_k(t_i, . . . ) be the k^th function that constitute the right-hand-side of the regression, k=1, . . . ,K

Let c_k be constants, k=1, . . . ,K

Let M be the number of basis functions.

Let N be the number of observations.

Let A be the design matrix of regression.

Let H be the right-hand-side of regression.

Let W be the weight-matrix.

Let Ω be the inverse of W.

Generic element in A is in the following form:
a_i,j=f_j(t_i, . . . ), i=1, . . . ,N, j=1, . . . M
Generic element in H is in the following form:

h i = ∑ k = 1 K ⁢ c k ⁢ q k ( t i , … ⁢ )
Generic element in W is in the following form:
w_i=w(t_i)
The coefficients of regression, β, an M-vector is given by the solution of the following linear equations:
[D^TD]·β=D^TH, where D=W·A   (12.2)
A constant term in basis functions f_j was not included but it may be included in (12.2).

• • 13.3 Standard Errors for Coefficients

Standard error for non-constant coefficient can be calculated in terms of design matrix and the weight matrix. The formula of standard error calculation is:

σ 2 ⁡ ( β j ) = ∑ i = 1 N ⁢ σ i 2 ⁡ ( ∂ β j ∂ h i ) 2 , with ⁢ ⁢ w = 1 σ ( 12.3 )
This formula reduces to

• σ²(β_j)=C_j,j, in general, covariance of β_i and β_j is C_i,j. Here C=(D^TD)⁻¹. The standard error for β_j is √{square root over (C_j,j)}.

14. Appendix E: Derive Y Estimated Value

• • 14.1 Calculate Estimated Value of Predicted Price Difference Y

Define a variable Y as the difference between trade t+1's transaction cost and market-adjusted price and the baseline price. Y is estimated by running Regression 7 on a set of independent variables. After a new trade occurs, using coefficients from overnight regression—Regression 7 multiplies related variables as the estimated value of Y, denoted as Ŷ=

∑ j = 1 9 ⁢ β ^ j × a j .
The detailed equation is as the following:
Ŷ=Reg7_Coef_x * X+Reg7_Coef_dx* X * I_d+Reg7_Coef_udx* X * U_d+Reg7_Coef_xlnft* X * T_d1+Reg7_Coef_xlnt* X * T_d2+Reg7_Coef_xig* X * IG_d+Reg7_Coef_xfq* X * T_s+Reg7_Coef_xsame* X * I +Reg7_Coef_xpos* X * Sum

14.2 Calculate Predicted Price

Variable Y is defined as the difference between trade t+1's transaction cost and market-adjusted price and the baseline price, which can be expressed in equation as:
Y=P_adj(t_i+1)−P5_adj(t_i−1)−MktA(t_i−5,t_i)−etf23(t_i+1)
Now, since the estimated value Y in previous section 4.4.1.3. has been calculated, the predicted price can be obtained according to the following:
PredPrice(t_i)=P_adj(t_i+1)−etf23(t_i+1)=P5_adj(t_i−1)+MktA(t_i−6,t_i−1)+Ŷ
where:
MktA(t_i−5, t_i)=etf23(t_i)+0.8 * etf23(t_i−1)+0.6* etf23(t_i−2)+0.4* etf23(t_i−3)+0.2* etf23(t_i÷4)
For Y only, trades that are eventually cancelled or replaced are not considered.

• • 14.3 Calculate New Price Difference X2 and New Predicted Price

Construct a new baseline price and average the predicted next-trade price as the following:

X₂=PredPrice(t_i)−PredPrice(t_i−1), predicted price PredPrice(t_i) is obtained from 4.4.1.4. as above

Use this new price difference X₂, and the coefficients from overnight regression—Regression 7 to generate a new estimated value of Y, denoted as Ŷ₂. The detailed equation is as the following:
Ŷ₂=Reg72_Coef_x2* X₂+Reg72_Coef_x2ud* X₂* U_d+Reg72_Coef_x21nft* X₂* T_d1+Reg72_Coef_x21nt* X₂* T_d2+Reg72_Coef_x2ig* X₂* IG_d+Reg72_Coef_x2fq* X₂* T_s+Reg72_Coef_x2pos* X₂ * Sum
Y₂ in the following equation is defined as:
Y₂=P_adj(t_i+1)−PredPrice(t_i−1)−etf23(t_i+1)
A new predicted price, denoted as PredPrice2(t_i) is determined in the following:
PredPrice2(t_i)=PredPrice(t_i−1)+etf23(t_i)+Ŷ₂(t_i)

15. Appendix F: Calculate ETF Betas

• • 15.1 Calculate Out-of-sample Betas

From overnight regression—Regression 2, saved 18 coefficients have been saved:

β_j, j=1, . . . , 18. Use these coefficients to calculate out-of-sample betas at the beginning of each day, and keep them consistent on intraday trades.
β_LQD=Reg2_Coef_sLQD +Reg2_Coef_sLQDmat10 * YTM₁₀+Reg2_Coef_sLQDrat * R +Reg2_Coef_sLQDmat10rat * YTM₁₀+Reg2_Coef_sLQDhy * H +Reg2_Coef_sLQDhyrat * H * R +Reg2_Coef_sLQDmat10hy * H * YTM₁₀+Reg2_Coef_sLQDmat10hyrat * H * YTM₁₀* R
β_HYG-LQD=Reg2_Coef_sHL +Reg2_Coef_sHLmat10 * YTM₁₀+Reg2_Coef_sHLrat * R+Reg2_Coef_sHLmat10rat * YTM₁₀+Reg2_Coef_sHLhy * H+Reg2_Coef_sHLhyrat * H * R+Reg2_Coef_sHLmat10hy* H * YTM₁₀+Reg2_Coef_sHLmat10hyrat* H * YTM₁₀

β TLT - IEI - Reg ⁢ ⁢ 2 ⁢ _Coef ⁢ _sLM10a * min ⁡ ( 20 , max ⁡ ( 0 , ytm - 10 ) ) 20 * ( SPrat ≥ 14 & ⁢ SPrat ∼ =. )

• • 15.2 Calculate Issue-Level Betas

Use the above out-of-sample betas and cell-level betas from Regression 4 and Regression 5 to calculate the new betas as:
β_l=Max(5,β_LQD * 0.4+Reg4_Coef_sLQD * 0.4)
β_h=β_HYG−LQD * 0.8+0.8 * (Reg5_Coef_sHL−β_HYG−LQD) *(1−0.2 * max(0−0.2 * max(0, Reg5_Se_sHL)))

β m = β TLT - IEI = { Reg2_Coef ⁢ _sLM10a * min ⁡ ( 20 , max ⁡ ( 0 , ytm - 10 ) ) 20 * ( SPrat ≥ 14 ⁢ ⁢ SPrat ∼ =. ) 0 , for ⁢ ⁢ all ⁢ ⁢ bonds ⁢ ⁢ rated ⁢ ⁢ less ⁢ ⁢ than ⁢ ⁢ A - or ⁢ ⁢ within ⁢ ⁢ 10 ⁢ ⁢ years ⁢ ⁢ of ⁢ ⁢ maturity

1. Phase Two Overview

Exemplary embodiments described herein provide the business requirements for implementing Phase Two of the Model Pricing. Except as otherwise stated, section numbers and appendices referred to within Phase Two refer to Phase Two section numbers and appendices. Model Pricing Phase Two embodiments may include:

• Developing an automated confidence measure that allows assessment of reliability of model prices produced in Phase One
• Providing exemplary functionality and controls for using the model price in market data ranking as one of the data sources among quotes, trades and evaluations
  • 1.1 Products in Scope

Phase Two covers products that produced a trade-based model price in Phase One, namely US Agency (AGN), Investment Grade (IG) and High Yield (HY) bonds. As described herein, Phase Two securities may have the same scope as implemented in Phase One, and may:

• Be USD denominated
• Be TRACE eligible
• Have at least ‘n’ trades in a 2-year trade history, where ‘n’ is configurable (initially set to 6). n=6 is a reasonable starting point since it is the minimum requirement to calculate adjusted price in Section 4.
• Not be a convertible bond, preferred stock, convertible preferred, or index linked note

The number of bonds covered at least one embodiment described herein regarding Model Pricing Phase Two is 11,917 in total, as shown in Table 10. In an exemplary embodiment, separate quotes-based and issuer-level models may be integrated into this functionality.

TABLE 100
Model Pricing Phase Two Scope

		IG	HY	Total

	Universe*	22,951	5,316	28,267
	Traded on TRACE	11,097	1,528	12,625
	Trade model prices	10,527	1,390	11,917
	No trade model, but either quote	6,726	2,089	8,815
	model or trade model for issuer
	Quote model	2,355	870	3,225
	Trade model for issuer	5,074	1,623	6,697
	Quote model only for issuer	2,601	990	3,591
	No models for any issue	4,057	1,159	5,216

Universe includes all corporate bonds with attribute data that, during 2013H1, were evaluated by IDC. Agencies, CBOs, CDs, Converts, Discount Notes, Equities, Index-linked Notes, Preferred Stock, Par Bonds, Treasuries may be excluded.

• • 2. Confidence/Quality Measure (Phase Two)

In an exemplary embodiment, an estimate of a 25-75 confidence interval surrounding an estimate of a bond's value is provided. This interval may be defined as a symmetric interval around the value estimate such that 50 percent of future trades are going to fall into. In other words, an estimate of 50% quantile through regression and an estimate 25% and 75% based on the 50% quantile estimate is provided. See Section 3 and Section 4 for calculation details.

FIG. 16 depicts an exemplary graph of a 75-25 confidence interval. The 25 and 75 graph-lines lines in FIG. 16 are the configurable values and we can alter their values in later step.

The output of confidence/quality measure below may generate a confidence interval width. Narrow intervals express greater confidence in the model price than wider intervals. The graph below illustrates the relationship between the confidence interval range and trade activity. From the graph, confidence interval is narrower at the point where trading volume is active. This is because the model has more trading information when the security is liquid, and the user is confident at this model price with more trading information and activities.

After running the overnight regression each day, the width of the confidence interval over next trade is provided in the table below:

Time since	75-25	90-10	95-5
last trade	interval	interval	interval	Ratios

<1 min	+/−9 cents	+/−27 cents	+/−44 cents	3×	5×
2 hours	+/−22 cents	+/−58 cents	+/−89 cents	2.6×	4×
2 weeks	+/−80 cents	+/−180 cents	+/−400 cents	2.3×	5×
Normal dist				1.9×	2.4×

This describes, for example at time since last trade is less than 1 minute, if model price is $100, then the 75-25 confidence interval may be 100±0.09, i.e., [99.91, 100.09]. The 90-10 and 95-5 confidence intervals are much wider than 75-25, due to fat tails. In an exemplary embodiment, using 75-25 may be preferred if confidence interval is over next trade price.

• • 2.1 Basic Workflows

Confidence intervals may be estimated at the same frequency as value estimates. In particular, a series of rolling window regressions may be run each evening and the betas from these regressions are used next day to calculate a pre-trade value estimate and confidence interval as of the time each trade. The betas from the last rolling window are stored and used to create value estimates that can be updated in response to new trades or the passing of time without a new trade. Like value estimates, confidence intervals may depend on the elapsed time since the last trade and on market movements since the last trade, as captured by ETF movements. In particular, confidence intervals generally widen as time passes without a trade, both in response to the passage of time and in response to cumulative changes in ETFs.

2.1.1 Logic Flowchart of Model Pricing Phase One & Phase Two

FIG. 17 depicts an exemplary flowchart showing the logic of real-time process of model pricing Phase One and Phase Two, and the connection between the two phases.

• • 2.2 Data Preparation

This section describes data needed in order to run overnight regressions and to update real-time confidence intervals in Model Pricing Phase Two. Some of them have been calculated and obtained in Model Pricing Phase One.

2.2.1 Data Dependencies

The sample includes up to two years of past data (this much data is really necessary—quantile regressions need large samples). Similar as Data Dependencies of Phase One in section 7, two-year data of the following may be needed:

• Reference Data
• TRACE Trade History
• Real-Time TRACE Trade Feed
• ETF Price History
• ETF Price Real-Time Ticking Feeds
• Model Pred Mid/Bid Prices
  2.2.2 Input Data Table

Table 11 shows variable names in regression functions, their variable names. There are two types of trades, defined as CUSIP * Second level, current trade and previous trade. The previous trade can be any type of trades, which includes small size trades. During out data time frame, the previous trade for the first trade of any CUSIP is defined as NULL.

For calculation of input data preparation, one way is to calculate these values for all trades on CUSIP * Second level first, aggregated multiple trades at each second. And then create two subsets: one for large dealer buy trades and the other for large interdealer trades. The previous trade of such a large trade can be either a large or a small size aggregated trade. To find the previous trade, one may go back one data element in time in the sorted data set with all trades. The current trade is the trade from to calculate surprise (calculation details in Section 2.2.3.4.), i.e., the dependent variable in quantile regression.

TABLE 11
Variable Definition

	Variable Names	Variable Names		Data
Objective	(in model)	(in Stata code)	Coefficient Name	Description

Transaction-cost-	Padj	f.adjp		Not
and-market-				Directly
adjusted future				Used
trade price (this is
calculated in
Model Pricing I)
Estimated value				For Current
(Model Pred				Trade
Bid/Mid Price, this
is calculated in
Model Pricing I)
Surprise for large	Sid	e2		For Current
interdealer trades				Trade
Surprise for large	Sdb	ebid2		For Current
dealer buy trades,				Trade
The integer for	d	bday		Between
each business day				Current and
				Previous
				Trade
The execution time	dbt	adjtime		Not
of each trade in				Directly
“business time”				Used
The difference in	Δt	fsadjt	CIQRegID_Coef_dt	Between
business time			CIQRegDB_Coef_dt	Current and
between the next				Previous
trade and the most				Trade
recent trade
The log difference	ln(Δt)	lnfsadjt	CIQRegID_Coef_lndt	Between
in business time			CIQRegDB_Coef_lndt	Current and
between the next				Previous
and most recent				Trade
trade
The log of one	ln(1 + Δd)	lnsbday	CIQRegID_Coef_lndbday	Between
plus the difference			CIQRegDB_Coef_lndbday	Current and
in business day				Previous
between the next				Trade
and the most
recent trade
The squared	(Δln(LQD))∧2	fsLQD	CIQRegID_Coef_lnLQD	Between
change in the log			CIQRegDB_Coef_lnLQD	Current and
LQD price				Previous
between the next				Trade
and most recent
trade
The squared	(Δln(AGZ))∧2	fsAGZ	CIQRegID_Coef_lnAGZ	Between
change in the log			CIQRegDB_Coef_lnAGZ	Current and
AGZ price				Previous
between the next				Trade
and most recent
trade (only for
Agency)
The squared	(Δln(HYG))∧2	fsHYG	CIQRegID_Coef_lnHYG	Between
change in the log			CIQRegDB_Coef_lnHYG	Current and
HYG price				Previous
between the next				Trade
and most recent
trade
The squared	(Δln(IEI))∧2	fsIEI	CIQRegID_Coef_lnIEI	Between
change in the log			CIQRegDB_Coef_lnIEI	Current and
IEI price between				Previous
the next and most				Trade
recent trade (only
for Agency)
The square of the	(Δetfpred2)∧2	fetf22	CIQRegID_Coef_etf23	Between
market adjustment			CIQRegDB_Coef_etf23	Current and
component used to				Previous
update for market				Trade
movements
between the next
and most recent
trades
The square of the	(Δetf2)∧2	etf22	CIQRegID_Coef_etf2	Between
market adjustment			CIQRegDB_Coef_etf2	Current and
component used to				Previous
update for market				Trade
movements
between the two
most recent trades
Indicator variable	Id	abstt	CIQRegID_Coef_indD	For
for the most recent			CIQRegDB_Coef_indD	Previous
trade having been				Trade
a dealer buy or
sell;
Indicator variable
for the most recent
trade having been
a client trade
Indicator variable	Ip	absdtt	CIQRegID_Coef_indP	For
for the most recent			CIQRegDB_Coef_indP	Previous
trade having been				Trade
a paired interdealer
trade
The average value	w	fq	CIQRegID_Coef_w	For
of the weight for			CIQRegDB_Coef_w	Previous
the trades in the				Trade
most recent
CUSIP*second
with a trade
The number of	Nt	trades	CIQRegID_Coef_Nt	For
trades in the most			CIQRegDB_Coef_Nt	Previous
recent				Trade
CUSIP*second
with a trade
The square of the	(P5adj(t) −	s5a5	CIQRegID_Coef_P5adj	For
change in the	P5adj(t-5))∧2		CIQRegDB_Coef_P5adj	Previous
baseline price Pb				Trade and 5
for the most recent				Trades
trade and for 5				Before It
trades ago
YTM30	YTM30	ytm	CIQRegID_Coef_ytm	Bond
			CIQRegDB_Coef_ytm
Sum of	w5	fq5	CIQRegID_Coef_w5	For
w variable for last			CIQRegDB_Coef_w5	Previous
5 CUSIP*seconds				Trade and 4
with trades (t-1 to				Trades
t-5)				Before It
The rating variable	R	rat	CIQRegID_Coef_R	Bond
R			CIQRegDB_Coef_R
The model-	ldb3 (or ldb, if	ldb3	CIQRegID_Coef_ldb3	For
estimated	ldb2 is not		CIQRegDB_Coef_ldb3	Previous
transaction cost	available)			Trade
from the most	ldb3 = min(0,			Valid ldb3
recent large dealer	ldb2)			at Previous
buy (for large				Trade Time
dealer buy trade,
tc3 is denoted as
ldb3; for large
interdealer trade,
tc3 is set as zero)
Intercept term of			CIQRegID_beta0
quantile regression			CIQRegDB_beta0
in Section 3

All input data passed to quantile regression (Section 3) may be aggregated trades but not atomic trades, on CUSIP*second level. It is acceptable if they are not real integers but with decimal points. For example, it is okay to have 0.667 under the column of indicator variable. In addition, when the input data compares two most recent trades, there is no requirement for the trade type, which means the trades are not only large dealer buy or interdealer trades, and they can be any size and type of trades.

2.2.3 Input Data Definition

This section defines input data in the table above in detail, and describes their calculations. Specifically, overnight regressions are run separately for two types of trades—large interdealer trades and large dealer buy trades. “Large” is defined as trades with size over $1,000,000. And two separate datasets are needed—one of large interdealer vs. model mid surprises, and one of large dealer buy vs. model bid surprises. Therefore, data and calculation results from Phase One of these two trades may be prepared and obtained before overnight regressions.

When a large interdealer trade or a large dealer buy trade comes in, store values of all the independent variables may be updated (required for overnight regressions in Section 3) of this trade. And set these values as a dataset of matrix, X, in the regression equation. To calculate the dependent variable, i.e., the surprise, only large interdealer and large dealer buy trade may be needed, thus, the dataset both for dependent variable and independent based on large interdealer and large dealer buy trade is set up. However, the confidence interval may be updated whenever a trade comes in at real time, regardless of large interdealer or large dealer buy trade. This means variables below may also be stored and used in real time calculation for the purpose of updating confidence intervals. But definition of distance in time may be different between data definition for overnight regression and data definition for real time calculation: all the time difference defined below for the purpose of overnight regression is the passage of time between two large interdealer trades (or two large dealer buy trades); while in real-time process, the passage of time may be defined as time distance between two any trades (regardless of large interdealer or large dealer buy trades). Also, the definition of indicator variable at real time for all trades may be different than the below: at real-time, it is defined the way as the table at Section 2.2.2.

In summary, here is the list of data needed to update and store when a large interdealer trade or a large dealer buy trade arrives (data of these two types of trades may be stored separately):

• Trade price, trade size: these two are used for calculation of average adjusted trade price in Section 2.2.3.3.
• S_id, S_db, Surprises: this is the dependent variable of the overnight regression, and this may be a data set (matrix Y) including all the large interdealer trades or large dealer buy trades information during the day based on CUSIP*second level.
• Execution time of the trade: executed time of this large interdealer trade (or large dealer buy trade).
• Business day and business time: calculation of these two is based on execution time of the trade, and calculation functions are in the following section 2.2.3.6.
• Δt, The difference in business time between this large interdealer trade (or large dealer buy trade) and the most recent large interdealer trade (or large dealer buy trade).
• 1n(Δt), The log difference in business time between this large interdealer trade (or large dealer buy trade) and the most recent large interdealer trade (or large dealer buy trade).
• 1n(1+Δd), The log of one plus the difference in business day between the next large interdealer (or large dealer buy) trade and most recent large interdealer (or large dealer buy) trade.
• (Δ1n(LQD))², The squared change in the log LQD price between this large interdealer trade (or large dealer buy trade) and most recent large interdealer (or large dealer buy) trade.
• (Δ1n(AGZ))², The squared change in the log AGZ price between this large interdealer trade (or large dealer buy trade) and most recent large interdealer (or large dealer buy) trade (only for Agency).
• (Δ1n(HYG))², The squared change in the log HYG price between this large interdealer trade (or large dealer buy trade) and most recent large interdealer (or large dealer buy) trade.
• (Δ1n(IEI))², The squared change in the log IEI price between this large interdealer trade (or large dealer buy trade) and most recent large interdealer (or large dealer buy) trade (only for Agency).
• (etf23)², The square of the market adjustment component used to update for market movements between this large interdealer trade (or large dealer buy trade) and most recent large interdealer trades (or large dealer buy trades); this is etf23 in Model Pricing Phase One, and calculation equations are in Model Pricing Section 4.6.3.3.
• (etf2)², The square of the market adjustment component used to update for market movements between the two most recent large interdealer (or large dealer buy) trades (the two previous trades before this new large interdealer or large dealer buy trade).
• I_d, I_p, Indicator variable for whether this is a large interdealer or large dealer buy trade.
• N_t, The number of trades at this executed second when the large interdealer or large dealer buy trade arrives (multiple trades could occur at the same executed second along with this large interdealer or large dealer buy trade); see more details at Section 2.2.3.8.
• w, The average value of the weight for the trades in the executed second when this recent large interdealer or large dealer buy trade arrives; calculation details are in the following section 2.2.3.9.
• YTM₃₀, The year to maturity of the security, definition is at Section 2.2.3.11.
• (P5adj(t)−P5adj(t−5))², The square of the change in the baseline price for this large interdealer trade or large dealer buy trade and for 5 trades (large interdealer or large dealer buy trade) ago
• ldb3, or ldb2 or ldb if ldb3 is not available, The model-estimated transaction cost from the most recent large dealer buy trade; for large interdealer trades, set ldb3=0, i.e., their transaction costs are set to zero

In the above items, from Δt to ldb3 together with the bond's rating variable R, all these variables may be included in the dataset as matrix X working as independent variables for the overnight regression at the end of the day. For agency, replace ETF tickers LQD with AGZ, HYG with IEI both in overnight regressions and in real-time calculation process.

2.2.3.1. Collapse Multiple Trades at CUSIP*Second

Similarly as Model Pricing Phase One, the data is collapsed to the CUSIP*second level in Phase Two as well. This means if multiple trades occurred in the same second, they are collapsed in the same second into an average price. For example, there is one model bid/mid price or average adjusted trade price for an executed second with a trade or multiple trades. Same as Phase One, trades are ordered within each issue based on execution time. For cases with multiple trades executed in a given second, trades are ordered by IssuePriceID. This is also the reason that in output files at Section 6, columns such as model prices, adjusted trade prices, etc., are displayed in bond-level output file but not trade-level output file. The result of these columns is aggregated trade result if multiple trades occurred in the execution second. In other words, a model price or adjusted price is not calculated for each trade but for per second.

2.2.3.2. Model Bid/Mid Prices

In Phase One, when new trade comes in or ETF price changes, model price is updated triggered by these two factors, and thus new model bid/mid price is produced. Model bid/mid price is stored whenever the model updates. To calculate the dependent variable for overnight regression, the model bid/mid price is sued right before the large interdealer trade or large dealer buy trade occurred, i.e., the last updated model bid/mid price before the large interdealer trade or large dealer buy trade comes in.

2.2.3.3. Average Adjusted Trade Price

Whenever a large interdealer trade or large dealer buy trade comes in, this average adjusted trade price is calculated by using the equation below. At real time, the average transaction-cost-adjusted price is within each second with a trade. For each CUSIP*second, take a weighted average of data for all large interdealer trades or large dealer buy trades executed that second. For example, at time t, there are T large interdealer trades at the executed second t denoted as t_ii=1,2, . . . T, the calculation is done as the following:

P adj = ln ⁡ ( lotsize ⁡ ( t 1 ) 100 ) * ( p ⁡ ( t 1 ) - tc ⁢ ⁢ 3 ⁢ ( t 1 ) ) + ln ⁢ ( lotsize ⁡ ( t 2 ) 100 ) * ( p ⁡ ( t 2 ) - tc ⁢ ⁢ 3 ⁢ ( t 2 ) ) + … ⁢ + ln ⁡ ( lotsize ⁡ ( t T ) 100 ) * ( p ⁡ ( t T ) - t ⁢ ⁢ c ⁢ ⁢ 3 ⁢ ( t T ) ) ln ⁡ ( lotsize ⁡ ( t 1 ) 100 ) + ln ⁡ ( lotsize ⁡ ( t 2 ) 100 ) + … ⁢ + ln ⁡ ( lotsize ⁡ ( t T ) 100 ) ( 2.1 )
where lotsize(t_i) is the size of large interdealer trade i, P(t_i) is the trade price of trade i, tc3(t₁) is the transaction cost of trade i.

In an exemplary embodiment, use ln(lotsize/100) weight averaging consistently for any aggregation in Phase One and Phase Two. Save this average adjusted trade price for the purpose of calculating dependent variable, i.e., the surprise, for overnight regression.

2.2.3.4. Surprise

After the average adjusted trade price is obtained for each large interdealer trade or large dealer buy trade, the difference is calculated between this average adjusted trade price and model price on CUSIP*second level, i.e., the surprise. Save all the values of surprise on CUSIP*second level during the day, and set up a dataset for it as matrix, Y, in the regression equation. This is used as the dependent variable in the quantile regression in Section 3.

For large interdealer trades, model mid price is used to calculate the surprise as the squared difference between the average large interdealer trade price at CUSIP * second t+1 and the mid model price after CUSIP*second t, updated for the market change between t and t+1. t+1 is current time if a large interdealer trade arrives now, and t is the most recent model mid price updated by t+1.

For large dealer buy trades, model bid price is used to calculate the surprise as the squared difference between the average large client trade price at CUSIP * second t+1 and the bid model price after CUSIP*second t, updated for the market change between t and t+1. t+1 is current time if a large dealer buy trade arrives now, and t is the most recent model bid price updated by t+1.

Model mid price and model bid price are calculated in Model pricing Phase One Section 4, and this price is updated whenever a new trade comes in, regardless of whether it is large interdealer trade or dealer buy trade or not. Then calculate the difference between the average adjusted trade price (in Section 2.2.3.3.) and the estimated value (model bid/mid price). Call this the surprise, and calculate its square as the following equation shows:
S_id(t+1)²=(P_avg(t+1)−Model Pred Mid Price(t+1))²   (2.2)
S_db(t+1)²=(P_avg(t+1)−Model Pred Bid Price(t+1))²   (2.3)
Thus, S_id—the surprise of all interdealer trades is difference between next price and mid model; S_db—the surprise of all dealer buys is the difference between next price and bid model. Model Pred Bid/Mid Prices are calculated in Model Pricing Phase One.

2.2.3.5. Execution Time

The time stamp of each trade, regardless of large interdealer or large dealer buy trade or not, of their execution time is used. Business time and business day may be calculated from this execution time.

2.2.3.6. Business Day and Business Time

The execution time of each trade, regardless of large interdealer or large dealer buy trade or not, is converted into “business time” in Model Pricing Phase Two. In order to calculate business time, business days (i.e., weekdays excluding bond market holidays) are numbered consecutively since the beginning of the sample. Then, business time equals to the integer for each business day added to

max ⁡ ( 0 , min ( 1 , [ seconds ⁢ ⁢ since ⁢ ⁢ 8 ⁢ ⁢ AM ⁢ ⁢ NY ⁢ ⁢ time ⁢ / ⁢ 3600 ⁢ / ⁢ 9 ) ] ) ) .

Business time is denoted as t, and business day is denoted as d. Business time can be decimal, while business day can only be integer.

For example:

• A trade at 12:30 PM on business day 3 would have business time 3.5.
• A trade between 5 PM on business day 3 and before 8 AM on business day 4 would have business time 4.0.
  Business time may adjust for daylight savings. Additionally, business days may be adjusted for holidays.

2.2.3.7. ETF Prices at Executed Time

In an exemplary embodiment, data is sampled every 15 minutes during regular equity trading hours to check ETF price changes, and this frequency could be increased in real time process. If ETF price changes from the previous 15 minutes when checked, the new ETF price is stored, at the same time model price from Phase One may be updated as market adjustments update between last updated time and now (triggered by ETF price changes).

In addition, current execution time is stored when with new ETF prices, and this execution time is converted into business time. Then the real time confidence interval can be updated based on this ETF price changes and the new business time.

2.2.3.8. Number of Trades

Count and save the number of trades, regardless of large interdealer or large dealer buy trade, in the most recent CUSIP*second with a large interdealer trade or large dealer buy trade, and this variable is denoted as N_t.

2.2.3.9. Average Weight

Calculate and save the average value of the weight for the trades in the most recent CUSIP * second (if multiple trades occurred at this executed second) with a large interdealer or large dealer buy trade as:

w _ = ∑ w ∑ N t ( 2.4 )
where

w = ln ⁡ ( Lotsize $100 ) ,
and N_t is defined as above.

2.2.3.10. Sum of Last 5 Average Weights

Calculate and save the sum of w variable for last 5 CUSIP*seconds with trades (t−1 to t−5) as:
w5=w(t−1)+w(t−2)+w(t−3)+w(t−4)+w(t−5)   (2.5)

2.2.3.11. Years To Maturity

Use YTM₃₀ in confidence interval calculations. It is defined as:
YTM₃₀=max(0,min(30,ytm))   (2.6)
where ytm is the years to maturity from Model Pricing Phase One. This calculation also equals to 10*YTM₁₀+20 * YTM₂₀, where YTM₁₀ and YTM₂₀ are defined in Model Pricing Phase One (YTM₂₀=min(20,max(0,ytm−10))/10).

3. Quantile Regressions for Confidence Interval Calculation

This section describes the methodology of running quantile regressions for confidence intervals. The confidence interval overnight regression only considers two types of trades: large interdealer trades and large dealer buy trades. However, at real time updates of confidence interval model is triggered by any types of trades.

• • 3.1 Estimate Confidence Interval

Once squared surprise is calculated for each CUSIP*second with large interdealer and or large dealer buy trades during the day as section 2.2.3.4. shows, a quantile regression is run with squared surprise as the matched dependent variable and the variables listed above in section 2.2.2. as the independent variables. Both the dependent variables and independent variables are dataset, i.e., two matrix (Y and X) including intraday data on CUSIP*second level. Two regressions may be needed here: one regression is run for large interdealer trades vs. model mid surprises and another for large dealer buys vs. model bid surprises.

Observations are weighted by

w = e - [ today - day ⁢ ⁢ of ⁢ ⁢ trade 3652.5 ] ( 3.1 )
Weighted observations in his quantile regression code may be used, though there is minimal difference and impact between weighted and unweighted observations in quantile regression.

Currently, there is a “weight” column in QRegression API code, but whether to implement it internally or not is pending. The quantile predicted by the regression is the 50^th percentile.

3.1.1 Regression 1: Calculate Betas and Predicted Values

3.1.1.1. Basis functions: Variables Designed to Capture Confidence Intervals in Regression 1

Input data including datasets of dependent variable and independent variables can be obtained from Section 2. Regressions are run separately by using two different datasets—one of large interdealer vs. model mid surprises, and one of large dealer buy vs. model bid surprises. The following independent variables are defined as for two consecutive trades of the same type, and time difference between two consecutive trades of the same type.

Excluding constant term, the number of basis functions is 16 (M=16, see Appendix A). Basis functions are identified as follows:

g₁(t_i, . . . )=Δt, days apart in decimal, for two consecutive trades of the same type, Δt and Δd are different

g₂(t_i, . . . )=1n(Δt)

g₃(t_i, . . . )=1n(1+Δd) , days apart in integer

g₄(t_i, . . . )=(Δ1n(LQD))², log change in price, squared

g₄(t_i, . . . )=(Δ1n(AGZ))², log change in price, squared, for Agency use AGZ instead of LQD

g₅(t_i, . . . )=(Δ1n(HYG))²

g₅(t_i, . . . )=(Δ1n(IEI))², for Agency use IEI instead of HYG

g₆(t_i, . . . )=(etf23)², etf23 change, squared (between current large interdealer/dealer buy trade and the most recent trade of the same type)

g₇(t_i, . . . )=(etf2)², etf2 change, squared (between two previous trades of current large interdealer/dealer buy trade, the same type as the current large interdealer/dealer buy trade)

g₈(t_i, . . . )=I_d, equals to 1 if trade t−1 is a large dealer buy trade; otherwise 0

g₉(t_i, . . . )=I_p, equals to 1 if trade t−1 is a large paired interdealer trade; otherwise 0

g₁₀(t_i, . . .)=N_t, this is an output from Section 2.2.3.8.

g₁₁(t_i, . . . )=w, this is an output from Section 2.2.3.9.

g₁₂(t_i, . . . )=w5, this is an output from Section 2.2.3.10.

g₁₃(t_i, . . . )=YTM₃₀, this is an output from Section 2.2.3.11.

g₁₄(t_i)=R, same as Model Pricing Phase One

g₁₅(t_i)=(P5adj(t)−P5adj(t−5))², baseline price is defined in the most recent Model Pricing Phase One Section 4.6.4.1.

g₁₆(t_i, . . . )=ldb3, this is min(0, ldb2), where ldb2 is obtained from Model Pricing Phase One for large dealer buy trades

f(t_i, . . . )=(S_id)² or (S_db)², dependent variable Y

3.1.1.2. The left-hand-side of the regression

The left-hand-side for this regression includes the squared surprise for large interdealer/dealer buy trades. Similarly as regression in Phase One, this regression is run on rolling 24-month windows of data. Coefficients from the regression run using data from t−24 months to t are applied to the variables from trades from month t+1 to yield and out-of-sample predicted value, see section for predicted value calculation below.

3.1.1.3. Outputs: Betas and Out-of-sample Predicted Value

The output from this regression is the betas and predicted values calculated out of sample.

V pred = β 0 + ∑ j = 1 16 ⁢ ⁢ β j ⁡ ( t ) × g j ⁡ ( s ) s > t ( 3.2 )

These predicted values are truncated at the 1^st and 99^th percentiles from the most recent month. A minimum of (0.05 points)^{{circumflex over (0)}2} is also applied, i.e., replace the value with 0.05² if it is less than that. The square root of this predicted value, √{square root over (V_pred)}, is the width of the 75-25 confidence interval around each value estimate (this square root of the predicted value is one-half of the confidence interval).

3.1.1.4. Intercept term of the regression

For quantile regression, the default may be in Stata, which use_const term. When doing prediction, include the intercept term, but use default method for prediction. So intercept term is included in quantile regression analysis. In an exemplary embodiment, the following codes from Stata .do file are used:

• cap qreg e2 fsadjt lnfsadjt lnsbday ldb3 fsLQD fsHYG fetf22 etf22 abstt absdtt fq fq5 ytm rat s5a5 trades if f.tt==0&f.dtt==0&fs.dt>0&f. fq>9.2&m>=‘m’-24&m<‘m’ [aw=w], nolog
• cap predict temp
• cap replace p1=temp if m==‘m’
  • 3.2 Summary of Outputs

Table 12 below is the summary of outputs from Section 3 quantile regression, which are used in Section 4 for real time confidence interval update.

TABLE 12
Output Summary from Quantile Regressions

	Regression
Objective	No./Function	Coefficient Name

Calculate predicted value and	Large	CIQRegID_beta0
confidence interval for model	Interdealer	CIQRegID_Coef_dt
mid price	Trade	CIQRegID_Coef_lndt
	Regression	CIQRegID_Coef_lndbday
		CIQRegID_Coef_lnLQD
		CIQRegID_Coef_lnHYG
		CIQRegID_Coef_etf23
		CIQRegID_Coef_etf2
		CIQRegID_Coef_indD
		CIQRegID_Coef_indP
		CIQRegID_Coef_w
		CIQRegID_Coef_w5
		CIQRegID_Coef_Nt
		CIQRegID_Coef_P5adj
		CIQRegID_Coef_ytm
		CIQRegID_Coef_R
		CIQRegID_Coef_ldb3
Calculate predicted value and	Large Dealer	CIQRegDB_beta0
confidence interval for model	Buy Trade	CIQRegDB_Coef_dt
bid price	Regression	CIQRegDB_Coef_lndt
		CIQRegDB_Coef_lndbday
		CIQRegDB_Coef_lnLQD
		CIQRegDB_Coef_lnHYG
		CIQRegDB_Coef_etf23
		CIQRegDB_Coef_etf2
		CIQRegDB_Coef_indD
		CIQRegDB_Coef_indP
		CIQRegDB_Coef_w
		CIQRegDB_Coef_w5
		CIQRegDB_Coef_Nt
		CIQRegDB_Coef_P5adj
		CIQRegDB_Coef_ytm
		CIQRegDB_Coef_R
		CIQRegDB_Coef_ldb3

4. Update Confidence Intervals in Real-Time

When new trades come in or ETF price changes, value estimates are updated as described at Section 4 in the Model Pricing Phase One, new values of the dependent and independent variables of the regression in 3.1.1.1. are calculated if necessary for new betas calculation, and the updated betas estimated from the prior evening are used to calculate the new confidence intervals as shown in 3.1.. Triggered by new trades or ETF price changes, both model price (value estimation) in the most recent Model Pricing Phase One at Section 4 and confidence interval may be updated. The new trade information may be used and new ETF prices may be used to re-calculate new model mid/bid price and new confidence interval. If the new trade is large interdealer or large dealer buy trades, then new values of the dependent and independent variables of the regression may be updated and stored for the overnight regression at the end of the day. Coefficient names are defined in Section 2.2.2.. Also, variable mapping between model and Stata coding are listed in the table at Section 2.2.2..

• • 4.1 Update Independent Variables at Real-Time

After the coefficients from overnight regression at Section 3 are obtained, confidence interval is updated with new betas when new trades arrive or ETF price changes at real time.

4.1.1 Collapse Multiple Trades at CUSIP*Second

Similarly as Model Pricing Phase One, the data is collapsed to the CUSIP*second level in Phase Two real-time calculation as well. This means if multiple trades occurred in the same second, they are collapsed in the same second into an average price. For example, there may be only one model bid/mid price or average adjusted trade price for an executed second with a trade or multiple trades. This is also the reason that in output files at Section 6, columns such as model prices, adjusted trade prices, etc. are displayed in bond-level output file but not trade-level output file. The result of these columns is aggregated trade result if multiples trades occurred in the execution second. In other words, a model price or adjusted price is not calculated for each trade but for per second.

4.1.2 RT Input Data

Similarly as the list at Section 2.2.3., at real-time whenever new trades come in or ETF price changes, all independent variables are updated and the new confidence interval are re-calculated by using coefficients from overnight regressions.

In summary, here is the list of data that may be needed to update and store when new trade arrives:

• Trade price, trade size: these two are used for calculation of average adjusted trade price in Section 2.2.3.3.; they are only stored and used if the new trade is a large interdealer or large dealer buy trade
• S_id, S_db, Surprises: this is the dependent variable of the overnight regression, and this may be a data set (matrix Y) including all the large interdealer trades or large dealer buy trades information during the day based on CUSIP*second level; this is only calculated and stored for large interdealer or large dealer buy trade
• Execution time of the trade: executed time of the new trade or new ETF price
• Business day and business time: calculation of these two is based on execution time of the trade, and calculation functions are in the following section 2.2.3.6.
• Δt, The difference in business time between this new trade and the most recent trade
• 1n(Δt), The log difference in business time between this new trade and the most recent trade
• 1n(l+Δd), The log of one plus the difference in business day between this new trade and most recent trade
• (Δ1n(LQD))², The squared change in the log LQD price between this new trade and most recent trade
• (Δ1n(AGZ))², The squared change in the log AGZ price between this new trade and most recent trade (only for Agency)
• (Δ1n(HYG))², The squared change in the log HYG price between this new trade and most recent trade
• (Δ1n(IEI))², The squared change in the log IEI price between this new trade and most recent trade (only for Agency)
• (etf23)², The square of the market adjustment component used to update for market movements between this new trade and most recent trade; this is etf23 in Model Pricing Phase One, and calculation equations are in the most recent Model Pricing Section 4.6.3.
• (etf2)², The square of the market adjustment component used to update for market movements between the two most recent trades (the two previous trades before this new trade)
• I_d, I_p, Indicator variable for whether this is a client trade, a large dealer buy or a paired interdealer trade; definition of this indicator variables is in Section 2.2.2. table
• N_t, The number of trades at this executed second when this new trade arrives (multiple trades could occur at the same executed second along with this new trade); see more details at Section 2.2.3.8.
• w, The average value of the weight for the trades in the executed second when this new trade arrives; calculation details are in the following section 2.2.3.9.
• YTM₃₀, The year to maturity of the security, definition is at Section 2.2.3.11.
• (P5adj(t)−P5adj(t−5))², The square of the change in the baseline price for this new trade and for 5 trades ago
• tc3, or tc if tc3 is not available, The model-estimated transaction cost from the most recent trade (Note: For large interdealer trade, they may be simplified as large unpaired interdealer trade, which has zero transaction cost; so this variable may be removed from the calculation for large interdealer trade)
  4.1.3 Update Independent Variables in RT Calculation

When new trade arrives or each ETF price changes, the intraday calculation is done by using the updated independent variables of the new trade (defined as above in 4.1.2.) or change of the ETF price
V_pred=+CIQRegID_Coef_beta0+CIQRegID_Coef_dt * Δt +CIQRegID_Coef_lndt * 1n(Δt) +CIQRegID_Coef_lndbday * 1n(1+Δd) +CIQRegID_Coef_InLQD * (Δ1n(LQD))², use +CIQRegID_Coef_lnAGZ * (Δ1n(AGZ))² in Agency +CIQRegID_Coef_lnHYG * (Δ1n(HYG))², use +CIQRegID_Coef_lnIEI * (Δ1n(IEI))² in Agency +CIQRegID_Coef_etf23 * (etf23)²+CIQRegID_Coef_etf2 * (etf2)²+CIQRegID_Coef_indD * I_d+CIQRegID_Coef_indP * I_p+CIQRegID_Coef_w * w+CIQRegID_Coef_w5 * w+CIQRegID_Coef_Nt * N_t+CIQRegID_Coef_P5adj * (P5adj(t)−P5adj(t−5))²+CIQRegID_Coef_ytm * YTM30+CIQRegID_Coef_R * R+CIQRegID_Coef_Idb3 * ldb3   (4.1) where baseline price is defined as

P ⁢ ⁢ 5 adj ⁢ ( t ) = P adj ⁡ ( t ) + P adj ⁡ ( t - 1 ) + P adj ⁡ ( t - 2 ) + P adj ⁡ ( t - 3 ) + P adj ⁡ ( t - 4 ) 5 ,
and all the independent variables are defined in Section 2.2.2. , Table 11.
4.1.4 Calculate the Width of CI

These predicted values are truncated at the 1^st and 99^th percentiles from the most recent month. A minimum of (0.05 points)^{{circumflex over (0)}2} is also applied, i.e., replace the value with 0.05² if it is less than that. The square root of this predicted value, √{square root over (V_pred)}, is the width of the 75-25 confidence interval around each value estimate (this square root of the predicted value is one-half of the confidence interval). For interdealer trades, value estimate is the model mid price; and for dealer buy trades, value estimate is the model bid price.

5. Model Output Files

Similarly as in Model Pricing Phase One, at four times of each trading day (i.e. 10 am, 12 pm, 3 pm and 4 pm), two output files may be generated (in Excel .csv format): bond-level output file and trade-level output file. The output files provide data analysis for Model Pricing, especially supporting Methodology to check the performance of the model. New fields are added at the end of the existing tables from Model Pricing Phase One Section 6, and are highlighted below.

• • 5.1 Bond-Level Output File

The bond-level output file may contain all the statistics data for each certain security, for Phase One it has: Model Price (Bid/Mid/Ask Price), New Price (Bid/Mid/Ask Price), Difference in Prices, Last 5 Trades' Price, Last 5 Transaction Cost Adjustments, Transaction Cost Coefficients, Market Adjustment Coefficients, Value Estimate Coefficients; for Phase Two it may add new columns as: Business Day, Confidence Intervals Coefficients. This file includes all the regression results generated while running the model. Table 13 below shows all the available fields in the bond-level output file:

TABLE 13
Available Fields of Bond-level Output File
Available Fields

Sector	Security ID	Security Description
Model Bid Price	Model Mid Price	Model Ask Price
New Bid Price	New Mid Price	New Ask Price
Diff in Bid Price	Diff in Mid Price	Diff in Ask Price
Last Trade Price	Last Second Trade Price	Last Third Trade Price
Last Fourth Trade Price	Last Fifth Trade Price	Last Transaction Cost Adj
Last Second Transaction Cost Adj	Last Third Transaction Cost Adj	Last Fourth Transaction Cost Adj
Last Fifth Transaction Cost Adj	Reg1_Coef_tt	Reg1_Coef_dtt
Reg1_Coef_ttfq	Reg1_Coef_dttfq	Reg1_Coef_fq
Reg1_Coef_ttpos	Reg1_Coef_dttpos	Reg1_Coef_ttposfq
Reg1_Coef_dttposfq	Reg1_Coef_ttrat	Reg1_Coef_ttmat15
Reg1_Coef_ttposrat	Reg1_Coef_ttposmat15	Reg1_Coef_ttfqrat
Reg1_Coef_ttfqmat15	Reg1_Coef_ttfqmat15rat	Reg1_Coef_dttfqrat
Reg1_Coef_dttfqmat15	Reg1_Coef_dttfqmat15rat	Reg1_Coef_ttposfqrat
Reg1_Coef_ttposfqmat15	Reg1_Coef_ttposfqmat15rat	Reg1_Coef_dttposfqrat
Reg1_Coef_ttposfqmat15	Reg2_Coef_sLQD	Reg2_Coef_sLQDmat10
Reg2_Coef_sLQDrat	Reg2_Coef_sLQDmat10rat	Reg2_Coef_sLQDhy
Reg2_Coef_sLQDhyrat	Reg2_Coef_sLQDmat10hy	Reg2_Coef_sLQDmat10hyrat
Reg2_Coef_sHL	Reg2_Coef_sHLmat10	Reg2_Coef_sHLrat
Reg2_Coef_sHLma10rat	Reg2_Coef_sHLhy	Reg2_Coef_sHLhyrat
Reg2_Coef_sHLmat10hy	Reg2_Coef_sHLmat10hyrat	Reg2_Coef_sLM10a
Reg3_Coef_spy3	Reg3_Coef_spy3	Reg4_Coef_col
Reg4_Se_sel	Reg5_Coef_coh	Reg5_Se_seh
Reg6_Coef_stc	Reg6_Se_stc	Reg6_Coef_etf2
Reg6_Se_etf2	Reg7_Coef_x	Reg7_Coef_dx
Reg7_Coef_udx	Reg7_Coef_xLnft	Reg7_Coef_xLnt
Reg7_Coef_xig	Reg7_Coef_xfq	Reg7_Coef_xsame
Reg7_Coef_xpos	Reg72_Coef_x2	Reg72_Coef_x2ud
Reg72_Coef_x2Lnft	Reg72_Coef_x2Lnt	Reg72_Coef_x2ig
Reg72_Coef_x2fq	Reg72_Coef_x2pos	Years-To-Maturity
Last Trade Adjusted Price	Last Second Trade Adjusted	Last Third Trade Adjusted
Padj1	Price Padj2	Price Padj3
Last Fourth Trade Adjusted	Last Fifth Trade Adjusted Price	Last 5 Average TCMA Price
Price Padj4	Padj5	P5adj
X	X2	PredPrice
PredPrice2	Business Day	CIReg1id_Coef_fsadjt
CIReg1id_Coef_Lnfsadjt	CIReg1id_Coef_Lnsbday	CIReg1id_Coef_fsLQD
CIReg1id_Coef_fsAGZ	CIReg1id_Coef_fsHYG	CIReg1id_Coef_fsIEI
CIReg1id_Coef_fetf22	CIReg1id_Coef_etf22	CIReg1id_Coef_abstt
CIReg1id_Coef_absdtt	CIReg1id_Coef_fq	CIReg1id_Coef_trades
CIReg1id_Coef_s5a5	CIReg1id_Coef_ytm	CIReg1id_Coef_fq5
CIReg1id_Coef_rat	CIReg1id_Coef_ldb3	CIReg2db_Coef_fsadjt
CIReg2db_Coef_Lnfsadjt	CIReg2db_Coef_Lnsbday	CIReg2db_Coef_fsLQD
CIReg2db_Coef_fsAGZ	CIReg2db_Coef_fsHYG	CIReg2db_Coef_fsIEI
CIReg2db_Coef_fetf22	CIReg2db_Coef_etf22	CIReg2db_Coef_abstt
CIReg2db_Coef_absdtt	CIReg2db_Coef_fq	CIReg2db_Coef_trades
CIReg2db_Coef_s5a5	CIReg2db_Coef_ytm	CIReg2db_Coef_fq5
CIReg2db_Coef_rat	CIReg2db_Coef_ldb3
		LID Surprise
LDB Surprise	Trade Execution Time	Trade Execution Time
		Difference
Trade Execution Time Log	Business Day Log Difference	Squared Change of Log LQD Price
Difference
Squared Change of Log AGZ Price	Squared Change of Log HYG Price	Squared Change of Log IEI Price
Pred Squared Change of	Squared Change of Market	Weight Average
Market Adjustment	Adjustment
Trade Counts	Squared Change of Baseline Price	YTM30
Sum of Weight Average for	Rating	Transaction Cost
Last 5 Trades
Note:
Last Trade Price is the most recent aggregated trade price, i.e., if there are multiple trade occurred in one second, Last Trade Price may display the weight-averaged aggregation of all trades in that 1 second. Years-To-Maturity may be calculated based on the most recent trade.
Trade Execution Time, Trade Execution Time Difference, Trade Execution Time Log Difference are in the format of business time (conversion method is at Section 2).
If the field is an aggregated trade variable, it may show the result after the most recent trade is occurred and averaged.

• • 5.2 Trade-Level Output File

The daily trade-level output file includes all the trades' data processed by the model in one day, and fields in this file are the same as columns shown in Trade Data Enhancements for IG/HY and Agencies respectively. Table 14 below shows all the available fields in the trade-level output file:

TABLE 14
Available Fields of Trade-level Output File
Available Fields

Side	Size	Trade Spread
Trade BM	Trade Time	Time Applied
Model Side Indicator	Model Paired Indicator	Matched Trade ID
Model Updated Time	Trade Yield	Trade Price
LQD Price	HYG Price	TLT Price
IEI Price	Model Paired	Trade Execution Time
Client Trade Indicator	Paired Trade Indicator

Trade Execution Time is in the format of business time (method of conversion is in Section 2), and it is different from the format of Trade Time, which has the format as mm/dd/yyyy hh:mm:ss.

6. Pricing Modes

Model Price may be used as a source of market data to produce the Continuous Price, and if model price is chosen as the market data, notifications of model price status may have an impact on continuous price and may be managed by the evaluator. Testing of model price may be independent, like testing of trade outliers. There may be three market data types of model price, added to the Market Data Ranking screen:

• High confidence of model price.
• Medium confidence of model price.
• Low confidence of model price.
  The evaluator can select which model price to be used in Market Data Ranking algorithm as a reference to continuous price. Model price confidence intervals typically degrade as a result of two primary factors:
• Time since last trade.
• Volatility in traded prices.

FIG. 18 depicts an exemplary flow chart of a high level workflow of how to use model price in Market Data Ranking. The general strategy for using the alternative plan may be:

• Calculate the model price, and test model price independently.
• Calculate the Confidence Interval and Confidence Group, and display on Quote screen.
• Use model prices of different confidence groups as separate types in market data ranking. The ranking is manually managed as a profile, as in USIG today.
• Allow the evaluator to manage notifications if model price is chosen as market data and with a suspect status.

7. Status Handling

Status may be implemented both on Dashboard and Worksheet. There is no screen or GUI specifically for Model Pricing, but notifications and status may be enhanced into Dashboard and Worksheet in different sectors, i.e., IG, HY and AGY.

• • 7.1 Dashboard Display
• Include Model notifications in Dashboard counts of Suspect and Warning notifications only if model price is chosen as the source of market data in Market Data Ranking algorithm.
• No change in rule that all Suspect conditions may need to be dealt with prior to release.
  • 7.2 Worksheet Changes
• Current Status columns (Status 3 PM, Status RT, Status 4 PM) may reflect top-level status of the evaluation, i.e., the status of the Continuous Price.
• No additional columns for the GUI.

8. Model Confidence Group

According to model performance by confidence interval, the model confidence group is divided into three sub-groups: High, Medium, and Low. Confidence interval is calculated by using predicted model price over the next trade price. After the overnight regression is run in Section 3, the width of confidence interval may be calculated. Rank the width from small to large and fill model price into the following three model confidence groups based on cutoff threshold values. Narrow CIs predict better relative performance by the model, which means model price lies in CI percentile of 0-25^th has high confidence. For example, the table below is shown Model Mid Price performance by confidence interval.

					Model	Eval
Confidence	CI	Prior	Model	Eval	% of	% of
Group	percentile	MSE	MSE	MSE	Prior	Prior

High	0-25th	0.15	0.10	0.27	65	176
Medium	25th-50th	0.31	0.17	0.35	55	112
	50th-75th	0.41	0.23	0.49	57	120
	75th-90th	0.60	0.40	0.92	66	152
	90th-95th	0.89	0.55	0.84	62	94
Low	95th-100	2.68	0.97	2.32	36	86
	No Model	NA	NA	NA	NA	NA

In the above table, CI percentile in 0-25^th may be considered as top group, 25^th-95^th is medium group, and the bottom group is in 95^th-100 CI percentile. In addition, there are some descriptions of some fields in the above table:

• The Model MSE of 0.10 for the high confidence group means that the model is off by around sqrt(0.10)=32 cents, in par terms, on average.
• All MSEs may include the change in the random walk price, so even a perfect model may not have an MSE of zero. In other words, knowing all past data and having the best possible model still might not let you perfectly predict the next traded price.
• “Prior” means the VWAP based on TRACE data.
  • 8.1 Setting the Confidence Group

The boundaries between the confidence groups (High, Medium, Low) may be defined by configurable threshold levels.

• High confidence prices are those where the CI is narrower than the High/Medium Group Threshold
• Medium confidence prices are those where the CI lies between the High/Medium Group Threshold and the Medium/Low Group Threshold
• Low confidence prices are those where the CI is wider than the Medium/Low Group Threshold.

In addition to the thresholds themselves, a range is defined around the threshold to control and stabilize movement between the groups. A price only moves into a new group when it crosses the furthest point in the range. For example, if the High/Medium Group Threshold=12c, a range is defined around this of ±2c. A High Confidence price becomes a Medium Confidence price when its CI widens to 14 c, while a Medium Confidence price becomes a High Confidence price when its CI narrows to 10c. By using this range, the movement between the groups is smoothed, and price oscillation from one group to another is avoided when their CIs are close to the threshold.

For each pricing method, i.e., IG, HY and Agency, there are two sets of threshold range on configuration screen. Each of them has both an upper level value and a lower level value. The previous rules of switching between pricing modes have been removed, however, the definition of the three model price confidence groups and the threshold may keep the same as examples below.

For example, there are current configuration cutoff values and threshold values for High-Medium group as [13, +2, −3]. If at Day 1, the start confidence interval value is 9, then there are the following examples:

• CI=9<13, then Group=High (Note: the cutoff value is only used on the first confidence interval on Day 1)
• CI=14<15, no change: Group=High
• CI=15<=15, then Group=Medium (15 is the margin value here, so use the lower confidence group)
• CI=18>15, no change: Group=Medium
  Another example is when confidence intervals become narrower and change from lower confidence group to higher confidence group:
• CI=18>13, then Group=Medium
• CI=12>10, no change: Group=Medium
• CI=10, no change: Group=Medium (10 is the margin value here, stay at the lower confidence group)
• CI=8, then Group=High
• CI=50<80, then Group=Medium (on Day 1, compare the CI value with the cutoff value, it's 80 in this case)
• CI=100<=100, then Group=Low (100 is the margin value here, use the lower confidence group)
• CI=101, no change: Group=Low
• CI=100, no change: Group=Low
• CI=50, no change: Group=Low (50 is another margin value here, stay at the lower confidence group)
• CI=49, then Group=Medium

There are three more examples on Day 1 and comparing the first CI value and the cutoff value (keep the same assumption that the cutoff and threshold values for High-Medium group are [13, +2, −3], for Medium-Low group are [80, +20, −30]:

• CI=90>80, then Group=Low; CI=12<13, then Group=High
• CI=90>80, then Group=Low; CI=13<=13, then Group=Medium
• CI=10<13, then Group=High; CI=80>=80, then Group=Low

Additionally, it is possible that confidence group may jump from high confidence group directly to low confidence group, or from low confidence group to high confidence group.

On the screen, the user is able to edit the cutoff threshold and also the upper and lower level of the range, so the range of the threshold equals to: cutoffs±upper/lower level value. Please see Section 10.2.1. Model Pricing Configurations under the tab of Confidence Group. Behavior of the groups are described below in Section 8.2.-8.4..

• • 8.2 Behavior of Top Group—High Confidence

Model Pricing in this group may be considered as high confidence. There may be a warning notification if bond moves out of top group, under such circumstance, the evaluator may actively manage their continuous pricing evaluation, and choose if they want to choose model price medium confidence group as market data source. There may also be a warning notification if bond moves into the top group, under this case, the evaluator may consider using model price high confidence group as one of market data sources.

• • 8.3 Behavior of Medium Group—Medium Confidence

Model Pricing in medium group may be considered as medium confidence.

• • 8.4 Behavior of Bottom Group—Low Confidence/No Model

Model Pricing in bottom group may be considered as very low confidence or no model price.

• • 8.5 Rules for Handling Suspect Prices
• A suspect price may not update the Published Price until the suspect condition is resolved.
• If Model Price is suspect and it is chosen as the market data, then Continuous Price is suspect until the notification is accepted/rejected.

9. Model Price Enrichment (Calculate Model Evaluations Value)

Full calculation of model evaluations may be performed and these evaluation values may be displayed on the Quote screen:

• Ask Px=2*MidPx−BidPx.
• Calculate Bid/Ask adjustments.
• Bid, mean and ask yields may be calculated from the prices above using the security's continuous pricing configurations.
• Bid, mean and ask spreads may be calculated using the security's continuous pricing configurations and benchmarks, using the same rules as continuous pricing, i.e.:
• If Pricing Anchor=Price or Yield, don't calculate the spread.
• If Pricing Anchor=Spread, then calculate the spread using the configured benchmark.

Bid/Ask Config (Type, Value)

Bid Px	Mean Px	Ask Px
Bid Yield	Mean Yield	Ask Yield	Price To config (Mat,
			Call, Worst)
			Redemption configs
			Calculation configs
Bid Spread	Mean Spread	Ask Spread	Benchmark Config (Curve)

Bid Px and Mean Px are inputs, and the rest of the grids are the outputs. By using the rules above, ask Px and yield, spread can be calculated and converted from price. Note that that model price may not tick with the Treasury curve. Model price may tick with ETFs (also new trades), and ETFs ticking is more frequent than that of the Treasury curve. Additionally, model pricing is price based, when the Spread/Yield is calculated, the current value of the curve is used, but it is not necessary to tick with the curve at real time.

• • 9.1 Published Evaluation and Pricing Output File

The final pricing output file that gets published from the pricing methods (Agencies, HY, IG) includes the Published Evaluation values. The calculation rules above may ensure that the Published evaluation fields for all securities based on a model price are complete.

• • 10. GUI Design and Functionality

All the changes specified in Model Pricing Phase Two are applied to US IG, US HY and Agency screens. All the fields displayed on Worksheet, Quote Market screen, Quote History screen and Model Details Screen are defined in the spreadsheet, which is in Appendix E.

• • 10.1 Model Details Screen

Model Pricing Phase One has introduced all the fields on the Worksheet, including the following:

• Model Bid/Mid Spread
• Model Bid/Mid Price
• Model/Eval Diff
• Model 3 PM Bid/Mid Price
• Model 4 PM Bid/Mid Price
• Model 3 PM Bid/Mid Spread
• Model 4 PM Bid/Mid Spread

In Phase Two, there may be no new fields added onto the Worksheet. However, one or more model variables may be displayed on a new screen, e.g., Model Details screen. Model Details screen may show all the important variables from Model Pricing Phase One and Phase Two. This screen may be found in each of the three systems, i.e., IG, HY and Agency, under the submenu of Market Data. The user can flip the pricing mode on Dashboard or Worksheet to show the evaluations at Real Time, 3 PM, or 4 PM. FIG. 19 depicts an exemplary pricing mode displayed on a Model Details screen. Provided below is a list of fields on Model Details screen:

• Model Rating Score
• Model YTM
• Model Updated Time
• Model Bid Price
• Model Mid Price
• Model Ask Price
• Model Bid Spread
• Model Mid Spread
• Model Ask Spread
• Model Bid Yield
• Model Mid Yield
• Model Ask Yield
• Model/Eval Diff
• Model Market Adjustment
• Model Trade-to-trade Change in Price
• Model Price Status
• Model 3 PM Bid/Mid/Ask Price
• Model 3 PM Bid/Mid/Ask Spread
• Model 3 PM Bid/Mid/Ask Yield
• Model 4 PM Bid/Mid/Ask Price
• Model 4 PM Bid/Mid/Ask Spread
• Model 4 PM Bid/Mid/Ask Yield
• Model Confidence Intervals
• Model Confidence Group
• Model 3 PM Confidence Intervals
• Model 3 PM Confidence Group
• Model 4 PM Confidence Intervals
• Model 4 PM Confidence Group
  Details of the above new fields are listed in the table below:

Field	GUI Name	Data Range	Example
Model	Model Rating	Variable R in Model	0.25
Rating Score	Score	Pricing Phase One
		[0, 1]
		Rating = 0 for bonds
		rated AA+ or above,
		1 for bonds rated CC
		or below, and is linear
		in credit rating
		between as (S&P
		numerical −3)/16,
		i.e., rat = 1 − max
		(0,min(1,
		(SPrat −3)/16)).
		R may be set to 0 in
		calculation of
		Agencies.
Model YTM	Model YTM	ytm = (maturity_date-	3.0061601642710474
		execution_date)/
		365.25 (using the
		most recent
		trade execution time
		as the execution_date
		in calculation)
Model	Model	Date and time	09/04/2014 08:33:47
Updated	Updated	(mm/dd/yyyy
Time	Time	hh:mm:ss)
Model	Model Bid	Positive floating	99.81561
Bid/Mid/Ask	Price	number	99.86360
Price	Model Mid		99.91159
	Price
	Model Ask
	Price
Model	Model Bid	Positive floating
Bid/Mid/Ask	Spread	number
Spread	Model Mid
	Spread
	Model Ask
	Spread
Model	Model Bid	Positive floating
Bid/Mid/Ask	Yield	number
Yield	Model Mid
	Yield
	Model Ask
	Yield
Model/Eval	Model/Eval	Floating number
Diff	Diff
Model	Model Mkt	Positive floating
Market	Adj.	number
Adjustment
Model	Model Px	Positive floating
Trade-to-	Change	number
trade Change
in Price
Model Price	Model Price	Good, Failed,	Suspect
Status	Status	Suspect, Warning
Model 3PM	Model Bid	Positive floating
Bid/Mid/Ask	Price	number
Price	Model Mid
	Price
	Model Ask
	Price
Model 3PM	Model Bid	Positive floating
Bid/Mid/Ask	Spread	number
Spread	Model Mid
	Spread
	Model Ask
	Spread
Model 3PM	Model Bid	Positive floating
Bid/Mid/Ask	Yield	number
Yield	Model Mid
	Yield
	Model Ask
	Yield
Model 4PM	Model Bid	Positive floating
Bid/Mid/Ask	Price	number
Price	Model Mid
	Price
	Model Ask
	Price
Model 4PM	Model Bid	Positive floating
Bid/Mid/Ask	Spread	number
Spread	Model Mid
	Spread
	Model Ask
	Spread
Model 4PM	Model Bid	Positive floating
Bid/Mid/Ask	Yield	number
Yield	Model Mid
	Yield
	Model Ask
	Yield
Model	Model CIs	Positive Integers	15
Confidence
Intervals
Model	Model	High, Medium, Low	Medium
Confidence	Confidence
Group	Group
Model 3PM	Model CIs	Positive Integers
Confidence
Intervals
Model 3PM	Model	High, Medium, Low
Confidence	Confidence
Group	Group
Model 4PM	Model CIs	Positive Integers
Confidence
Intervals
Model 4PM	Model	High, Medium, Low
Confidence	Confidence
Group	Group

Descriptions and functionality of these fields are provided in the following sub-sections.

10.1.1 Model Rating Score:

Model Rating Score is defined and calculated in Model Pricing Phase One, which converts S&P Rating (or Moody's or Fitch Rating) to a numerical value between 0 and 1. Rating =0 for bonds rated AA+ or above, 1 for bonds rated CC or below, and is linear in credit rating between as (S&P numerical−3)/16, i.e., rat=1-max(0,min(1,(SPrat-3)/16)). R may be set to 0 in calculation of Agencies.

10.1.2 Model YTM:

Model YTM is defined and calculated in Model Pricing Phase One. ytm=(maturity_date-execution_date)/365.25(using the most recent trade execution time as the execution_date in calculation).

10.1.3 Model Updated Time:

Model Updated Time is defined in Model Pricing Phase One. Model Updated Time shows the time when model price is updated. The format of this field is defined as Date and Time (mm/dd/yyyy hh:mm:ss).

10.1.4 Model Bid/Mid/Ask Price/Spread Yield:

• Model Bid/Mid/Ask Price: Model Bid/Mid Price is calculated in Model Pricing Phase One, and Model Ask Price is defined and calculated in Model Pricing Phase Two Section 9. This is the real time model price.
• Model Bid/Mid/Ask Spread: Model Bid/Mid/Ask Spread is calculated based on model price and calculation is described in Model Pricing Phase Two Section 9. This is the real time model spread.
• Model Bid/Mid/Ask Yield: Model Bid/Mid/Ask Yield is calculated based on model price and spread, and the calculation is described in Model Pricing Phase Two Section 9. This is the real time model yield.
  10.1.5 Model/Eval Diff:

Model/Eval Diff is defined as the difference between model price and evaluation price at real time.

10.1.6 Model Market Adjustment:

Model Market Adjustment is defined and calculated in Model Pricing Phase One, which is denoted as etf23. And the calculation is described in Model Pricing Phase One Section 4.6.3..

10.1.7 Model Trade-to-trade Change in Price:

Model Trade-to-trade Change in Price is defined and calculated in Model Pricing Phase One, which is denoted as Δp.

10.1.8 Model Price Status:

Model Price Status is defined in Model Pricing Phase Two Section 11.1.3. with four values to show the status of model pricing: Good, Failed, Suspect and Warning.

10.1.9 Model 3 PM Bid/Mid/Ask Price/Spread/Yield:

Model 3 PM Bid/Mid/Ask Price/Spread/Yield is defined as Model Bid/Mid/Ask Price/Spread/Yield at 3 pm mode.

10.1.10 Model 4 PM Bid/Mid/Ask Price/Spread/Yield:

Model 4 PM Bid/Mid/Ask Price/Spread/Yield is defined as Model Bid/Mid/Ask Price/Spread/Yield at 4 pm mode.

10.1.11 Model Confidence Intervals:

Model Confidence Intervals show the results from regressions at Section 2 at real time, the confidence interval width:

• Model CIs: Model confidence interval width termed in price (cents), e.g. 15 (in price term, i.e., cents).
  10.1.12 Model Confidence Group:

Model Confidence Group shows which confidence group the bond may be located, based on confidence interval width calculated from Section 2 and confidence threshold in Section 4 at real time, which is defined on the screen as:

• Model Confidence Group: Model confidence group, e.g. High, Medium, Low.
  10.1.13 3 PM/4 PM CIs and Confidence Group.

New fields may include:

• Model 3 PM/4 PM Confidence Intervals.
• Model 3 PM/4 PM Confidence Group.
  These fields are defined similarly as real time Model Confidence Intervals and Model Confidence Group under 3 pm or 4 pm mode.
  • 10.2 Quote Market Screen—New Fields

FIG. 20 depicts an exemplary Quotes Market Data screen for each system, i.e., IG, HY and AGY for display of model price and model evaluations. In an exemplary embodiment, only the most recent model price may be displayed on the Quote Screen and positioned at the top row on the screen. There may be no display of model price ticks. The following fields may be displayed for each model price:

• Model Updated Time—The time when model price gets updated.
• Source Type—Model.
• Source Feed—Name of Omega source feed for published model price—check with Dev (Alex and Ling), the name of the feed.
• Bid/Mid/Ask Price, Implied Bid/Mid/Ask Price, IDCO Bid/Mid/Ask Price: Under the source of model pricing, these columns may show model bid/mid/ask price.
• Implied Bid/Mid/Ask Yield, IDCO Bid/Mid/Ask Yield: Under the source of model pricing, these columns may show model bid/mid/ask yield calculate using the rules in Section 9; Bid/Mid/Ask Yield may be blank under the source of model pricing.
• Implied Bid/Mid/Ask Spread, IDCO Bid/Mid/Ask Spread: Under the source of model pricing, these columns may show model bid/mid/ask spread; Bid/Mid/Ask Spread may be blank under the source of model pricing.
• 3 PM/4 PM Bid/Mid/Ask Price/Yield/Spread: these fields may show model bid/mid/ask price/yield/spread at 3 pm or 4 pm mode.
  10.2.1 Button Behavior

Accept: Accepts the most recent model price, clearing and dismissing any notification on the security due to the selected market data.

Reject: Rejects the most recent model price, clearing any notification on the security due to the selected market data and going back to the last good model price.

Apply as Eval: The evaluator may select a line that may be used for the evaluation and click Apply as Eval. Particularly, model price may be automatically ticking with each institutional trade, and the evaluator can use this button to apply model price as the evaluation. Note that this may behave the same way as any manually applied trade or quote, in the sense that the market data ranking may only consider data that comes in after the apply time of the model price, when deciding whether new data may replace the manually applied model price.

The rest of the buttons on the screen, i.e., Cancel, Set Default Source, Unset Default Source, Quote Entry, may be grayed out when a model price is selected. Note Model Price sensitivity condition may last until it's accepted/rejected or the next institutional trade occurs. The maximum time of Model Price sensitivity condition may last until the end of the day.

10.2.2 Market Data Ranking Profile

FIG. 21 depicts an exemplary investment grade data ranking profile screen. The evaluator can set up model pricing as one of the market data sources on Market Data Ranking Profiles screen in each system, i.e., IG, HY and AGY. Model Price High Confidence Group, Model Price

Medium Confidence Group, and Model Price Low Confidence Group may be shown under “Unused Data Types” and can be selected to Data Ranking tab as a source of market data. The configuration of the three Model Price Confidence Groups can be done on the configuration screen at sector level, which is shown in Section 10.3.1.2.

• • 10.3 Quote History Screen

FIG. 22 depicts an exemplary Quote History screen for each system, i.e., IG, HY and AGY, displaying model price and model evaluations. Similarly defined as the Quote screen, only the most recent model price may be displayed on the Quote History Screen and positioned at the top row on the screen. There may be no display of model price ticks.

• • 10.4 Event Log

FIG. 23 depicts an exemplary event log. One row is added in the event log each time an institutional trade causes model price ticking, and meanwhile model price is the driver of the evaluation (i.e., model price is selected as the market data source). In addition, capture the price once an hour and display as “Hour (10 AM) Price”. The purpose of this record is to show the hourly price between institutional trades, which may occur hours away with each other. This hourly price is recorded regardless of whether model price is selected as market data source.

• • 10.5 Configuration Screens

There are two types of configuration screens: Model Pricing Configurations, which is added to the existing tabs from Phase One and this is on model level; and Model Notifications Configurations, which is added to the existing tabs on the existing Configuration screen in each system, i.e., IG, HY and AGY.

10.5.1 Model Pricing Configurations

Configurations on this screen are all model level and are sectors of CORP, AGENCY and INACTIVE. Values are configurable under each sector. There are two new tabs added to the existing Model Pricing Configurations screen from Phase One, which are Confidence Interval and Confidence Group.

Confidence Interval:

FIG. 24 depicts an exemplary model pricing configuration screen for a confidence interval. This screen enables Methodology to configure definition of large trade's size, quantile regression type, truncation requirements, and minimum points requirements.

Confidence Group

FIG. 25 depicts an exemplary model pricing configuration screen for a confidence group. On this screen, Methodology and evaluator can change the cutoff values and threshold range of the three confidence groups, i.e., High, Medium and Low. Definition and examples of confidence groups are described in Section 9. In an exemplary embodiment, all the margin values of the range are inclusive; in other words, if the confidence interval equals the margin value of the range or on the border, then it may belong to the lower confidence group.

10.5.2 Model Notifications Configurations

FIG. 26 depicts an exemplary sector configuration screen for model notifications. Configurations on this screen may be added to the existing tabs in each system, i.e., IG, HY and AGY under sectors. This new tab enables Methodology and the evaluator to change the default tolerance of Model Notifications. For example, FIG. 26 is a screenshot to add the Model Notifications tab onto the existing USIG Sector Configuration screen.

11. Notifications

In an exemplary embodiment, none of the existing notifications applied to trades or quotes may be applied to model price. Notification details may be displayed on Inbox of each pricing system, i.e., IG, HY and Agency. Model Price may be tested independently, and notifications may only be applied if model price is chosen as the market data.

• • 11.1 Suspect

There is one Model Price Notification. If the test is failed, it may generate a suspect notification. If the notification is acknowledged, then the evaluator may not get a new notification until a new institutional trade comes in.

11.1.1 Model Sensitivity to Δ Institutional Trade Px

There may be a Large Change in Model Sensitivity suspect notification if:

• there is a large difference between changes of model mid price and changes of institutional trade price since the last institutional trade, i.e., the difference between the deltas is more than X (X is configurable)

In this case, the evaluator may be able to verify model price and the cause of this large difference. When comparing the changes of model mid price and changes of institutional trade price, the same time period may be used. For example, if our new trade happens at time t, and the last institutional trade time is at t−1, then the changes of trade price may be Δ_p=P(t)−P(t−1). And model bid price at t and t−1 may be used to calculate the changes in the model, i.e., Δ_M=M(t)−M(t−1). M(t) and M(t−1) are model mid prices triggered by trade at t and t−1. The sensitivity test passes if the difference between changes of model mid price and changes of institutional trade price is less than X. For example, at time t, Δ_P(t)−Δ_M(t)>X have been tested (when test fails, notification is issued). The suspect notification is cleared automatically when a new institutional trade arrives, causing the test to be run again, and the test passes. For example, at time t+1, the differences are again calculated as Δ_P(t+1)=P(t+1)−P(t), and Δ_M(t+1)=M(t+1)−M(t). If ΔP(t+1)−Δ_M(t+1)<X, then the suspect notification may be cleared. Alternatively, the evaluator can accept the suspect model price manually to clear the notification. Model Price sensitivity condition may last until it's accepted/rejected or the next institutional trade occurs. The maximum time of Model Price sensitivity condition may last until the end of the day.

• • 11.2 Warnings
    11.2.1 Big Change in Confidence Interval

If confidence interval moves sharply, the evaluator may receive a warning notification if:

• confidence interval moves from one confidence group to another, e.g., confidence interval jumps from medium confidence group to high confidence group.
  Under such circumstances, the evaluator may have a warning notification as big change in confidence interval. The test may be based on confidence interval threshold values defined in Section 8.1. to decide if model price has been moved from one confidence group to another.
  11.2.2 First Model Price

There may be a warning notification when the first model price is available. This is for new issued bonds, which have had at least six trades. No action is required for this warning notification. And the purpose of this notification is to let the evaluator know that model price is available and good to use from today. This warning notification may be cleared automatically at the end of the day. This is in the Model Pricing Phase One's spec, Section 4.1., Minimum Requirements of Intraday Calculation. To calculate the first model price, at least six trades may be needed to run the overnight regression. And to generate model price at real-time, besides these six trades, the seventh trade may be needed to happen the next day to trigger the intraday calculation on model price. For example, there are several possible cases:

• When there is at least six trades today, the overnight regression is run by using these trades and saving the coefficients. The next day, the first model price may not be calculated until a new trade comes in.
• When there is at least six trades today, the overnight regression is run by using these trades and saving the coefficients. The next day, there may not be a new trade but the ETF price changes. In this case, the first model price may not be calculated.
• The first model price may only be calculated when there is at least six trades today, and the overnight regression is run by using these trades and saving the coefficients. And the seventh trade is the next day (or several days later). Then the coefficients may be used to generate the first model price.
  • 11.3 Calculation Failure

Calculation Failure may be applied to model price. Rules of handling calculation failure notifications are:

• Use same failure notifications as IG.
• Failure Notifications may be counted on Dashboard.
  • 11.4 Model Pricing Status

There is a Model Price Status column on Model Details screen with four possible values to show the status of model pricing: Good, Failed, Warning, and Suspect. The status of each model price may be maintained, but (like outliers in trades and quotes), notifications may only be generated if the model price is chosen to be applied by the Market Data Ranking rules. If this model price is suspect, it generates the notification, and the Continuous Price is suspect until the notification is accepted or rejected. The evaluator may clear all notifications before release.

• • 11.5 Notification Details

Description
(headline)	Type	Reason (details)	Cause	Actions	Screen

Large	Suspect:	[security ID] [security	During the same	The	Worksheet
Change in	Worksheet	description] has a	time period, the	evaluator
Model		large difference	changes of model	may be
Sensitivity		between changes of	price (use mid price)	able to
		model price and changes	and changes of	verify
		of institutional trade	institutional trade	model
		price and the difference	price has a large	price and
		is more than [X].	difference and break	the cause
			the default	of this
			tolerance.	large
				difference.
Calc Failure	Calc	[security ID] [security	The system is	The	Worksheet
	Failure:	description] has calc	unable to calculate	evaluator
	Worksheet	failure.	a security and the	may either
			calculation library	correct the
			may return a failure.	security's
			The possible reasons	configuration,
			of calc failure may	modify
			be the same as	underlying
			defined in IG.	assumptions, or
				enter a manual
				price only
				quote for the
				security.
Big Change	Warning:	[security ID] [security	Model Price is more	The evaluator	Worksheet
in	Worksheet	description] has moved	confident as new	may reevaluate
Confidence		from [X] confidence	trades come in or	whether to
Interval		group to [Y]	less confident as	use model
		confidence	time passed without	price as a
		group.	any trade, i.e., the	market data
			confidence interval	source
			is widen out.
First Model	Warning:	[security ID] [security	This is for new	No action	Worksheet
Price	Worksheet	description] has the	issued bond with at	required.
		first model	least six trades. This	The evaluator
		price available.	warning notification	can go to market
			may alert the user	data ranking
			that the first model	profile to set
			price is available to	model price as
			be considered in	the driver of the
			market data source.	evaluation.

12. Configurations

Configurations in this section are applied to all the three pricing systems—IG, HY and Agency. For each system, there may be one configuration screen.

• • 12.1 Configurable Numbers and Functions
• The type of confidence interval is configurable. Currently, all the examples used in apply to a 25-75 confidence interval. A 10-90 or 5-95 confidence interval can be used later.
• The type of quantile regression is currently using 50^th percentile. This is configurable.
• Predicted values are truncated at the 1^st and 99^th percentiles from the most recent month, and these numbers are configurable.
• A minimum of (0.05 points)^{^2} is applied, and this is also a configurable number.
• The cutoff of the confidence group by using CI percentile may be configurable.
  • 12.2 Configuration Screens

FIG. 27 depicts an exemplary model pricing configuration screen for a confidence interval.

FIG. 28 depicts an exemplary sector configuration screen for model notifications.

13. Appendix A: Regression Framework and Formulae

In this Appendix address regression frameworks are addressed in general and regression formulae applied to TC model and Market Adjustment. Note that all regressions involved may be weighted regressions. Also note that the design matrix and the right-hand-side of regressions include 1^st differences, except for the constant term in design matrix.

• • 13.1 Assumptions and General Settings

A few assumptions are made as basis of framework and general settings for TC model and Market Adjustment applications are provided. Regressions are run in rolling windows. The generic form of a rolling window is [t−24, t] with t being a time unit in month. Assuming that observations come with execution times {t_i}. The execution times are also used to calculate 1^st differences. Let p_t denote the price at execution time t. Then the 1^st difference for price is calculated according to the following:
p_ti−p_ti−1=Δp_iϵΔp↦t_i−1<t_i;t_i,t_i−1ϵ[t−24,t];(t_i−1,t_i)∩[t−24,t]=0    (10.1)
(t_i−1,t_i)∩[t−24,t]=0 means there is no execution between t_i−1 and t_i. 1^st differences for other quantities are also calculated according to rules above. Note that 1^st difference calculations are based on grouping according to certain id's.

• • 13.2 Regression Formulae and Components
    The following notations are defined as follows:
    Let f_j(t_i, . . . ) be the j^th basis function at time t_i.
    Let q_k(t_i, . . . ) be the k^th function that constitute the right-hand-side of the regression, k=1, . . . ,K.
    Let c_k be constants, k=1, . . . ,K
    Let M be the number of basis functions.
    Let N be the number of observations.
    Let A be the design matrix of regression.
    Let H be the right-hand-side of regression.
    Let W be the weight-matrix.
    Let Ω be the inverse of W.
    Generic element in A is in the following form:
    a_i,j=f_j(t_i, . . . ), i=1. . . , N , j=1, . . . M
    Generic element in H is in the following form:

h l = ∑ k = 1 K ⁢ c k ⁢ q k ( t i , … ⁢ )
Generic element in W is in the following form:
w_i=w(t_i)
The coefficients of regression, β, an M-vector is given by the solution of the following linear equations:
[D^TD]·β=D^TH, where D=W·A   (10.2)
A constant term was not included in basis functions f_j but it may be included in (10.2).

14. Appendix B: Blended Model—18 Betas Model

• • 14.1 Inputs
    There may be two time variable inputs:
• t is the time at which the bond is evaluated.
• s is the time of the most recent human evaluation.

For mids, there are 5 primary inputs:

• M_t^M, the model mid price at time t.
• M_s^M, the model mid price at time s.
• C_t^M, the continuous pricing mid price at time t.
• C_s^M, the continuous pricing mid price at time s.
• E_s^M, the evaluation at time s.
  For bids, there are another 5 primary analogous inputs:
• M_t^B, the model bid price at time t.
• M_s^B, the model bid price at time s.
• C_t^B, the continuous pricing bid price at time t.
• C_s^B, the continuous pricing bid price at time s.
• E_s^B, the evaluation at time s.

In addition, there may be several secondary inputs used for calculating betas in Section 15.5 below:

• Confidence intervals for the mid and bid model output at time t and s.
• Values for the most recent trade prices for the ETFs used by the corporate model (LQD, HYG, IEI, TLT) at times s and t (For Agency, use ETF tickers AGZ, IEI, TLT).
• Years to maturity and next call.
• Credit rating.
  • 14.2 Outputs

For each issue, the system may produce a blended mid and bid price and an updated confidence interval for each:

• Blended Bid Price
• Blended Mid Price
  • 14.3 Variable Definition

In an exemplary embodiment, this is the mapping of variable names in the model.

• • 14.4 Method

For each of blended mid and bid prices, the method may estimate 9 parameters, for mids:
B_t^M=E_s^M+β₁^M(M_t^M−M_s^M)+β₂^M(M_s^ME_s^M)+β₃^M(C_t^M−C_s^M)+β₄^M(C_s^M−E_s^M)+β₅^M(M_t^B−M_s^B)+β₆^M(M_s^B−E_s^M)+β₇^M(C_t^B−C_s^B)+β₈^M(C_s^B−E_s^M)+β₉^M(E_s^BE_s^M)
and for bids:
B_t^B=E_s^B+β₁^B(M_t^M−M_s^M)+β₂^B(M_s^M−E_s^B)−β₃^B(C_t^M−C_s^M)+β₄^B(C_s^M−E_s^B)+β₅^B(M_t^B−M_s^B)+β₆^B(M_s^BE_s^B)+β₇^B(C_t^B−C_s^B)+β₈^B(C_s^B−E_s^B)+β₉^B(E_s^M−E_s^B)

The betas may be configured by methodology by using an upload function, since the 18 betas are different bond by bond. The betas above may be estimated using a past sample of data, using a linear regression on the above equations, where the Bs may be substituted with a measure of future mid/bid prices. The betas may be modeled to be a function of the secondary inputs, and these functions may also contain parameters to be estimated.

• • 14.5 Upload Blended Px Betas

FIG. 29 depicts an exemplary upload button. There may be an upload button for methodology to manually upload the 18 betas on bond level, as the betas are calculated and different bond by bond. This button may be available on system level, one for each of AGN, IG, HY, and the top menu option as shown in FIG. 29. Upload Blended Px Betas menu is under the Maintenance menu for each pricing system.

FIG. 30 depicts an exemplary screen of upload blended price betas. The “Import Items” button enables the user to load the file where the blended price betas have been saved.

FIG. 31 depicts an exemplary new tab added on the screen of Security Details as “Blended Px Betas” and display CUSIP with 18 betas. This is applied to all the three pricing systems, i.e., IG, HY and Agency.

15. Appendix C: Historical Data Dependencies

This section describes historical data that may be needed in order to run quantile regression for confidence intervals and linear regression for blended model.

• • 15.1 Historical Data for Quantile Regression

Two-year data of the following fields may be needed to run quantile regression in Section 3.

15.1.1 Reference Data

Reference data in the model includes only the following fields:

• CUSIP.
• Maturity—enriched to Years to Maturity, YTM₃₀.
• Ratings—enriched to rating buckets.

Historical reference data is not available. For purposes of historical inputs into the regressions, current reference data may be used for all bonds. Note that the reference data at time of trade may be used.

15.1.2 TRACE Data

Two years trade data may be needed. The trade data may be transformed into the same format that the History service retrieves on a going forward basis, in order to be populated and retrieved by the service on Day 1. From Phase One, the following trade-level data may be captured—these fields are used for GUI purposes—and may be included in the history service:

• MODEL_UPDATED_TIME.
• MODEL_SIDE_INDICATOR.
• MODEL_PAIRED_INDICATOR.
• MODEL_PAIRED.
• MODEL_PRICE_CHANGE.
• MODEL_OBSERVATION_WEIGHT.
• MODEL_BID_PRICE.
• MODEL_ASK_PRICE.
• MODEL_MID_PRICE.
• MODEL_OUTOFSAMPLE_TC.
• MODEL_TRUNC_OS_TC.
• MODEL_RESCALED_TC.
• MODEL_FINAL_TC.

In addition to the highlighted fields above (needed for linear regression), the following 4 fields may also be needed for calculating the confidence interval:

• MODEL_ADJ_PRICE
• MODEL_LDB2
• MODEL_PRED_MID_PRICE
• MODEL_PRED_BID_PRICE

These fields may have been added to Phase One already, such that it may not be necessary to back-populate them from Phase One go-live day to Phase Two go-live day. Historical values may be included.

15.1.3 Bond Data Betas

For the first Day 1 CI regression, the bond-level ETF betas (5 per day per bond) may be needed and 2 years worth of history. The 5 bond-level ETF betas that may be needed to calculate etf2 and etf23 are:

• beta_l (this is final LQD beta calculated by using beta_LQD and the cell-average coefficient).
• beta_h (this is final HYG-LQD beta calculated by using beta_HYG-LQD and the cell-average coefficient).
• beta_m (this is final TLT-IEI beta calculated by using beta_TLT-IEI).
• Reg6_Coef_etf2 (Issue-level market adjustment coefficient, from Regression 6).
• Reg6_Se_etf2 (Issue-level market adjustment standard error, from Regression 6).
  15.1.4 ETFs Price Data

Two-year past ETFs price history sampled every 15 minutes may be needed, for LQD and AGZ. This may be used to attach the trade data. This requirement may already be met for Phase One.

• • 15.2 Historical Data for Blended Model (Linear Regression)

One-year data of the following fields may be needed to run linear regression in Section 5.

15.2.1 TRACE Data

One-year TRACE trade may be needed, including trade price for each large interdealer trade and each large dealer buy trade. This data may already be available. In addition, the evaluation price may be attached at time of trade to each trade. For historical purposes, there may only be 3 PM and 4 PM prices. The logic may be as follows:

• Any trade executed prior to 3 PM gets the previous business day's 4 PM evaluation.
• Any trade executed between 3 PM (inclusive) and 4 PM gets the 3 PM evaluation.
• Any trade executed after 4 PM (inclusive) gets the 4 PM evaluation.
  15.2.2 Model Price

One-year Model Mid/Bid Price may be used for the same large interdealer trade and large dealer buy trade. These may be captured in the history above (16.2.1)

15.2.3 Confidence Interval

One-year confidence interval at the time of each historical large interdealer and large dealer buy trade may be needed for all dates up to Go Live -1.

15.2.4 LQD (AGZ for Agencies) Price at time of evaluation

One-year LQD price may be needed at the time of each evaluation:

• For the 3 pm evaluation, find the ETF price prior to 3 pm.
• For the 4 pm, evaluation, find the ETF price prior to 4 pm.

16. Appendix D: Downgrade List of Agency and IG Notifications

There are two downgrade lists below for Agency and IG notifications respectively. If it is a “Yes” in Downgrade column, then when model price changes, these notifications may be downgrade from suspect to warnings following rules in Section 9.5. If it is a “No” in Downgrade column, then when model price moves, these notifications may stay as suspect. If it is a “N/A” in Downgrade column, then these notifications do not relate to model price or do not have a model price, so they may not change their notifications with model price. In an exemplary embodiment, only suspect notifications may be downgraded, all the warnings may remain the same.

• • 16.1 Downgrade List of Agency Notifications

Downgrade	Description
?	(headline)	Type	Reason (details)

Yes	Outlier	Suspect:	Outlier [Trade Side] trade
	Buy/IDB	Market	received for [Trade Size] of
	Trade	Data	[CUSIP] at [Trade
			Timestamp]: [IDCO
			Bid Spread] to
			[IDCO Benchmark]
			([IDCO Bid Spread -
			New Bid Spread])
N/A	Incomplete	Suspect:	[Curve Name] is missing
	Curve	Curve	sufficient data for points:
	Notification		<List of missing CMT points>
N/A	Discount Rate	Suspect:	Rate for [Month] of [New
	<Minimum	Rates	Rate] is less than the minimum
			[Minimum Rate]
N/A	Discount Rate	Suspect:	Outlier quote received from
	Outlier	Rate	[Source]:
		Quotes
N/A	Insufficient	Suspect:	Insufficient market data
	Data for	Rates	to calculate Agency
	Discount		Discount Rates scale
	Rates Scale
Yes	Negative	Suspect:	Negative yield(s) detected for
	Yield	Evaluation	[CUSIP]:
N/A	Unchanged	Suspect:	Spread has not changed for a
	Curve Spread	Evaluation	particular ‘curve point’
			on the issuer curve.
N/A	Unchanged	Suspect:	Spread has not changed for
	Curve Spread		a particular ‘curve point’
			on the issuer curve.

• • 16.2 Downgrade List of IG Notifications

Downgrade	Description
?	(headline)	Type	Reason (details)

Yes	One-Sided	Suspect:	A one-sided ask quote for security
	Ask Quote	Market	[security ID] [security description]
		Data	was received from default source [default
			source name]. Review the
			default source and determine if it may
			be changed.
Yes	Outlier	Suspect:	The incoming [market data type] for
		Market	[security ID] [security description] has
		Data	exceeded the outlier threshold of [X]
			by [Y].
Yes	Stale Default	Suspect:	The default source [source name] has
	Source	Market	exceeded the stale threshold of [X].
		Data	Currently, it has been stale for [Y]
			days.
Yes	Same-level	Suspect:	Notification may indicate that the
	Default Source	Market	market data was previously rejected
	Quotes	Data	source is sending unchanged level.
Yes	Assign Parent	Suspect:	The market data score for security
		Parent/Child	[security ID] [security description] has
			dropped below the suspect
			configurable threshold of [10]
			does not have a parent assigned.
			Review the security and assign it to a
			parent if possible.
Yes	MD Score	Suspect:	The Market Data Score has fallen
	Fallen Below	Configuration	below a certain threshold that is
	a Certain		configurable by the user.
	Threshold
Yes	Child BM	Suspect:	Child [security ID] [security
	Change	Parent/Child	description] has changed to the
			[benchmark] benchmark. Verify the
			Parent relationship is accurate or find
			a new Parent.
No	Child	Suspect:	Child [security ID] [security
	Corporate	Parent/Child	description] has had a corporate
	Action		action. Verify the Parent relationship
			is accurate or find a new Parent.
Yes	Child Credit	Suspect:	Child [security ID] [security description]
	Rating Change	Parent/Child	has changed to a [rating agency]'s [rating level]
			rating. Verify the Parent relationship is accurate
			or find a new Parent.
Yes	Child	Suspect:	Child [security ID] [security description]
	Redemption	Parent/Child	has a change in redemption date. Verify the
	Date Change		Parent relationship is accurate or find a new
			Parent.
Yes	Large	Suspect:	The difference in benchmark yield between
	Parent/Child	Parent/Child	Child [security ID] [security description] and
	BM Change		Parent [security ID] [security description] is
			now [Y], which exceeds the change of
			threshold of [X].
Yes	Parent BM	Suspect:	Parent [security ID] [security description]
	Change	Parent/Child	has changed to the [benchmark] benchmark.
			Verify the dependent security relationships
			are accurate or find a new Parent for the
			dependent securities.
Yes	Parent Credit	Suspect:	Parent [security ID] [security description]
	Rating Change	Parent/Child	has changed to a [rating agency]'s [rating level]
			rating. Verify the dependent security
			relationships are accurate or find a new Parent
			for the dependent securities.
Yes	Parent	Suspect:	Parent [Parent security ID] [Parent
	Matured	Parent/Child	security description] has matured.
			Select another Parent for [security
			ID] [security description].
Yes	Parent	Suspect:	Parent [security ID] [security description]
	Redemption	Parent/Child	has a change in redemption date. Verify
	Date Change		the dependent security relationships are
			accurate or find a new Parent for the
			dependent securities.
Yes	Stale Offset	Suspect:	The offset of Child [security ID] [security
		Parent/Child	description] and Parent [security ID]
			[security description] has exceeded the stale
			offset threshold of [X]. It has been stale for
			[Y] days.
Yes	Stale Parent	Suspect:	Parent [security ID] [security description]
		Parent/Child	has exceeded the stale Parent threshold of
			[X]. It has been stale for [Y] days.
No	Manager	Suspect:	(see details in section 18.3 and 20.3.2)
	Approval	Configuration
	Required
No	Security	Suspect:	[security ID] [security description] has
	Called	Worksheet	been called.
No	Corporate	Suspect:	[security ID] [security description] has
	Action	Worksheet	had a corporate action.
No	Defaulted	Suspect:	[security ID] [security description] has
	Security	Worksheet	defaulted.
Yes	Undefaulted	Suspect:	[security ID] [security description] has
	Security	Worksheet	un-defaulted {security no longer in
			default}.
Yes	Big Mover—	Suspect:	Manual quote of [security ID]
	Manual	Worksheet	[security description] is [Y] different
	Enterred		from last published price; exceeded
	Quotes		the big mover tolerance [X].
Yes	Big Mover—	Suspect:	Enterred guidance of [security ID]
	Manual	Worksheet	[security description] is [Y] different
	Enterred		from last published price; exceeded
	Guidance		the big mover tolerance [X].
No	Big Mover—	Suspect:	[security ID] [security description] has
	Jump to Par	Worksheet	moved to par or redemption price
			since the last published price.
Yes	Unchanged	Suspect:	[security ID] [security description] has
	Evaluation	Worksheet	not changed for [X] days, exceeding
			the unchanged threshold of [Y] days.
Yes	Retail Bond:	Suspect:	The incoming [market data type] for
	Interdealer/	Market	[security ID] [security description] has
	Dealer	Data	exceeded the outlier threshold of [X]
	Buy/Default		by [Y].
	Source
	Outliers

17. Appendix E: Fields of Worksheet and Quote screens

The spreadsheet below is an exemplary list of the fields displayed on Worksheet, Main Quote Market screen, Quote History screen, and Model Details screen.

				Quote	Model
Field	Phase	WS	Quote	History	Details
Model Rating Score	1				x
Model YTM	1				x
Model Updated Time	1		x	x	x	add to Quote
						screen, remove
						from WS
Model Bid Spread	1	Model	Implied Bid	x	x	keep bid/mid in
		Bid	Spread			worksheet
		Spread	IDCO Bid
			Spread
Model Mid Spread	1	Model	Implied Mid	x	x
		Mid	Spread
		Spread	IDCO Mid
			Spread
Model Ask Spread	1		Implied Ask	x	x
			Spread
			IDCO Ask
			Spread
Model Bid Yield	1		Implied Bid		x
			Yield
			IDCO Bid
			Yield
Model Mid Yield	1		Implied Mid		x
			Yield
			IDCO Mid
			Yield
Model Ask Yield	1		Implied Ask	x	x	remove from WS
			Yield
			IDCO Ask
			Yield
Model Bid Price	1	Model	Bid Price	x	x
		Bid	Implied Bid
		Price	Price
			IDCO Bid
			Price
Model Mid Price	1	Model	Mid Price	x	x
		Bid	Implied Mid
		Price	Price
			IDCO Mid
			Price
Model Ask Price	1		Ask Price	x	x	keep bid/mid in
			Implied Ask			worksheet
			Price
			IDCO Ask
			Price
Model/Eval Diff	1	x			x	keep on WS
Model Market	1				x
Adjustment
Model Trade-to-trade	1				x
Change in Price
Model Price Status	1				x	Status of model
						price
						independent of
						whether or not
						it's being used
Model 3PM	1	x	x	x	x	keep bid/mid in
Bid/Mid/Ask Price						worksheet
Model 4PM	1	x	x	x	x	remove from WS
Bid/Mid/Ask Price
Model 3PM	1	x	x	x	x	keep bid/mid in
Bid/Mid/Ask Spread						worksheet
Model 4PM	1	x	x	x	x	remove from WS
Bid/Mid/Ask Spread
Model 3PM	1		x	x	x	remove from WS
Bid/Mid/Ask Yield
Model 4PM	1		x	x	x	remove from WS
Bid/Mid/Ask Yield
Model Confidence	2				x	remove from WS
Intervals
Model Confidence	2				x	remove from WS
Group
Model 3PM	2				x	remove from WS
Confidence Intervals
Model 4PM	2				x	remove from WS
Confidence Intervals
Source Type	2		x	x		remove from WS
Source Feed	2		x	x		remove from WS
Model 3PM	2				x	remove from WS
Confidence Group
Model 4PM	2				x	remove from WS
Confidence Group

Embodiments comprise computer components and computer-implemented steps that will be apparent to those skilled in the art after reviewing the description herein. For example, calculations and communications can be performed electronically, and results can be displayed using a graphical user interface.

An overview of an exemplary such system is depicted in FIG. 32. Computers 100 communicate via network 110 with a server 130. The computers 100 may be any device operable to provide the functionality disclosed herein, including communicating with the one or more servers and/or other client devices, displaying information with one or more interface screens, collecting information from users thereof, retrieving data, storing data, etc. For example, the computers 100 may be a mobile phone, a smart phone or tablet, a personal computer (PC), as well as any dedicated computer apparatus. The front-end functionality may be provided with a browser or any other network communication application, or with special purpose software or “apps” designed specifically for accessing and providing the features disclosed herein. A plurality of sources of data 120-121 also communicate via network 110 with a server 130, processor 150, and/or other components operable to calculate and/or transmit information. Server(s) 130 may be coupled to one or more storage devices 140, one or more processors 150, and software 160.

Exemplary computers 100 according to at least one embodiment are shown. In one embodiment, the computers 100 include a bus or other communication mechanism for communicating information between components of the computers 100, and the processor 150 coupled with the bus for processing the information. The computers 100 may also include a main memory, such as a random access memory (RAM) or other dynamic storage device (e.g., dynamic RAM (DRAM), static RAM (SRAM), and synchronous DRAM (SDRAM)), coupled to the bus for storing information and instructions to be executed by processor 150. In addition, the main memory may be used for storing temporary variables or other intermediate information during the execution of instructions by the processor 150. The computers 100 may further include read only memory (ROM) or other static storage device (e.g., programmable ROM (PROM), erasable PROM (EPROM), and electrically erasable PROM (EEPROM)) coupled to the bus for storing static information and instructions for the processor 150. The at least one computer readable medium or memory may have stored thereon programmed instructions and/or contain data structures, tables, records, or other data described herein.

The computers 100 may also include a disk controller coupled to the bus to control the one or more storage devices 140 for storing information and instructions, such as a hard disk, and a removable media drive (e.g., floppy disk drive, read-only compact disc drive, read/write compact disc drive, compact disc jukebox, tape drive, and removable magneto-optical drive). The storage devices 140 may be added to the computers 100 using an appropriate device interface (e.g., small computer system interface (SCSI), integrated device electronics (IDE), enhanced-IDE (E-IDE), direct memory access (DMA), or ultra-DMA).

The computers 100 may also include special purpose logic devices (e.g., application specific integrated circuits (ASICs)) or configurable logic devices (e.g., simple programmable logic devices (SPLDs), complex programmable logic devices (CPLDs), and field programmable gate arrays (FPGAs)) designed to perform as the components described herein.

The computers 100 may also include a display controller coupled to a bus to control a display, such as a liquid crystal display (LCD), for displaying information via the one or more interface screens disclosed herein to a user thereof. In one exemplary embodiment, the computers 100 include at least one input device, such as a keyboard or a pointing device, for a computer user to interact with the computers 100 and to provide information/instructions to one or more processors, e.g., the processor 150. The pointing device, for example, may be a mouse, a trackball, a pointing stick, a track pad, a touch screen, etc. In addition, a printer may provide printed listings of data stored and/or generated by the computers 100.

The computers 100 generally perform a portion or all of the processing steps disclosed herein in response to the processors, e.g., the processor 150, executing one or more sequences of one or more instructions contained in a memory, such as the main memory. Such instructions may be read into the main memory from another computer readable medium, such as a hard disk or a removable media drive. The instructions stored may be in any form, including without limitation executable code, scripts, interpretable programs, dynamic link libraries (DLLs), Java classes, application program interfaces (APIs), complete executable programs, or a combination thereof.

The computers 100 may also include a communication interface coupled to the bus. The communication interface provides a two-way data communication coupling to the network 110 that is connected to, for example, a local area network (LAN), or to another communications network, such as the Internet. For example, the communication interface may be a network interface card to attach to any packet switched LAN. As another example, the communication interface may be an asymmetrical digital subscriber line (ADSL) card, an integrated services digital network (ISDN) card, or a modem to provide a data communication connection to a corresponding type of communications line. Wireless links may also be implemented. In any such implementation, the communication interface sends and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

The network 110 typically provides data communication through one or more networks to other data devices. For example, the network 110 may provide a connection to another computer through a local network (e.g., a LAN) or through equipment operated by a service provider, which provides communication services through a communications network. The local network and the communications network use, for example, electrical, electromagnetic, or optical signals that carry digital data streams, and the associated physical layer (e.g., CAT 5 cable, coaxial cable, optical fiber, etc). Moreover, the network 110 may provide a connection through a LAN or wireless network to a mobile device, such as a personal digital assistant (PDA), smartphone, laptop computer, or any other type of client device.

The system features may generally operated or otherwise made available by one or more providers via the one or more server 130. Some of the features of the system may be provided in conjunction with a third party or parties. For example, a provider may obtain information in connection with the one or more features through third party data providers, such as from a regulatory database (e.g., as the SEC's EDGAR), a commercial data provider (e.g., Bloomberg, Reuters, etc.), or any other public or private data source (e.g., securities exchanges). The provider server or servers may be coupled to one or more third party servers 130 and/or databases 140.

The provider or a third party may also allow companies, investors, intermediaries, or other users of the system to exchange trading or pricing information regarding trades or securities on one or more electronic trading platforms, marketplaces, and/or exchanges, such as via an electronic communication network (ECN), etc. In this instance, the system may further have access to one or more exchange or marketplace servers. That is, the computers 100 may receive data regarding trade orders directly from an exchange server or indirectly from a provider server.

The system may be implemented over any type of communications network, such as a local area network (LAN), a wide area network (WAN), the Internet, a telephone network (POTS), a wireless network, including cellular and Wi-Fi networks, or combinations of wired and/or wireless networks. For example, the computers 100 may access the servers 130 directly over a LAN/WAN 110. Alternatively or additionally, computers 100 may access the servers 130 indirectly over a LAN/WAN 110. The computers 100 are preferably configured or otherwise capable of transmitting and/or receiving communications to and/or from the one or more servers 130, including any items of data discussed herein. This may be accomplished with a communication interface that enables communication with a similarly equipped server computer, wirelessly, wired, or a combination thereof. In at least one embodiment, the computers 100 generally provide the front-end functionality and one or more servers 130 provide the back-end functionality discussed herein.

Calculations described herein, and equivalents, are, in an embodiment, performed entirely electronically. Other components and combinations of components may also be used to support processing data or other calculations described herein as may be evident to one of skill in the art. Server 130 may facilitate communication of data from a storage device 140 to and from processor(s) 150, and communications to computers 100. Processor 150 may optionally include or communicate with local or networked storage (not shown) which may be used to store temporary or other information. Software 160 can be installed locally at a computer 100, processor 150 and/or centrally supported for facilitating calculations and applications.

For ease of exposition, not every step or element of the present invention is described herein as part of a computer system, but those skilled in the art will recognize that each step or element may have a corresponding computer system or software component. Such computer system and/or software components are therefore enabled by describing their corresponding steps or elements (that is, their functionality), and are within the scope of one or more embodiments of the present invention.

Moreover, where a computer system is described or claimed as having a processor for performing a particular function, it may be understood by those skilled in the art that such usage may not be interpreted to exclude systems where a single processor, for example, performs some or all of the tasks delegated to the various processors. That is, any combination of, or all of, the processors specified in the description and/or claims could be the same processor. All such combinations are within the scope of one or more embodiments of the invention.

Alternatively, or in combination, processing and decision-making may be performed by functionally equivalent circuits such as a digital signal processor circuit or an application specific integrated circuit.

Many routine program elements, such as initialization of loops and variables and the use of temporary variables, are not described herein. Moreover, it may be appreciated by those of ordinary skill in the art that unless otherwise indicated, the particular sequence of steps described is illustrative only and can generally be varied without departing from the scope of the invention. Unless otherwise stated, the processes described herein are unordered—that is, the processes can be performed in any reasonable order.

All steps described herein may be understood by those skilled in the art as being capable of implementation in one or more embodiments by software, where feasible. Moreover, such software may be understood by those skilled in the art to be storable on a non-transitory computer readable medium and implementable by one or more computer processors.

While certain exemplary aspects and embodiments have been described herein, many alternatives, modifications, and variations may be apparent to those skilled in the art. Accordingly, exemplary aspects and embodiments set forth herein are intended to be illustrative, not limiting. Various modifications may be made without departing from the spirit and scope of the disclosure.