# HSBC Instrument Specifications .pdf

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HSBC Instrument Specifications

September 2007

CONFIDENTIAL INFORMATION

Copyright © 2007 QuIC Financial Technologies Inc.

All rights reserved.

Document Revision: 2.47

HSBC Instrument Specifications

Document version: 2.47

DO NOT COPY OR DISTRIBUTE

TERMS OF USE

This document, the contents of this document and the software and script

technology described by this document (collectively the Property) are

Copyright © 2007, QuIC Financial Technologies Inc. (QuIC), and constitute

proprietary and confidential information of QuIC that is subject to protection

under Canadian and international trademark and copyright legislation. QuIC

reserves all rights in and to the Property.

Any copying, reproduction, distribution, transmission or disclosure of all or any

part of this document or its contents, in any form or by any means, is strictly

prohibited without the prior written consent of QuIC.

This document is provided to you (as an individual and as a representative of

your company) subject to QuIC’s standard Confidentiality Agreement, Evaluation

License and Agreement, Software License and Support Agreement or similar

document, and you agree to the terms of use of the Property as laid out therein

respectively. Notwithstanding the terms and conditions as may be applicable to

this document, you agree to treat the Property as confidential information unless

advised otherwise by QuIC in writing.

While every effort has been made to ensure that the information contained in this

documentation is correct, QuIC does not warrant the information is free of errors

or omissions, unless agreed to otherwise in writing. The information contained in

this document is subject to change without notice.

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CONTACTING QUIC

Head Office

QuIC Financial Technologies Inc.

1095 W. Pender Street, Suite 1105

Vancouver, BC V6E 2M6

CANADA

EMEA

QuIC Financial Technologies (UK) Ltd.

1 Cornhill

London, EC3V 3ND

UNITED KINGDOM

Research & Development

QuIC Financial Technologies Inc.

3553 – 31st Street NW, Suite 225

Calgary, AB T2L 2K7

CANADA

Americas

QuIC Financial Technologies Inc.

39th Floor, 245 Park Avenue

New York, NY 10167

USA

Asia Pacific

QuIC Financial Technologies Inc.

One Marina Boulevard #28-00

SINGAPORE 018989

www.quic.com

Within North America:

Outside North America:

1.877.689.1888

1.306.337.1446

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CONTENTS

1

INTRODUCTION .................................................................................. 12

1.1

Purpose of This Document .......................................................... 12

1.2

Document Audience ................................................................... 12

1.3

Where to Go for Help ................................................................. 12

1.4

Document Version History .......................................................... 13

2

SIGN-OFFS ........................................................................................ 21

3

PROJECT SCOPE ................................................................................. 22

3.1

PFE Simulation .......................................................................... 22

3.1.1

Equity Risk Simulation ................................................... 22

3.1.2

Credit Spread Simulation ............................................... 26

3.1.3

Jumps ......................................................................... 26

3.1.4

Default ........................................................................ 26

3.1.5

Basket ......................................................................... 26

3.2

Pricing Models ........................................................................... 26

3.2.1

Equity ......................................................................... 26

3.2.2

Inflation....................................................................... 27

3.3

Financial Instruments ................................................................. 27

3.4

QuiC Financial Engineers per Instrument / Model ........................... 29

4

INSTRUMENT SPECIFICATIONS ............................................................ 30

4.1

Cross Instrument Inputs ............................................................. 30

4.1.1

Map Inputs: MultiLeg ..................................................... 30

4.2

American Exercise Vanilla Equity Option ....................................... 30

4.2.1

Description................................................................... 30

4.2.2

Performance Options ..................................................... 37

4.2.3

Finite Difference Solution Preferences .............................. 38

4.2.4

Transaction File Inputs .................................................. 38

4.2.5

Auxiliary Transaction Data File Inputs .............................. 41

4.2.6

Market Data Curves ...................................................... 43

4.2.7

Definition of Daycounts .................................................. 49

4.2.8

Testing Methodology ..................................................... 50

4.3

European Exercise Vanilla Equity Option ....................................... 50

4.3.1

Description................................................................... 50

4.3.2

Settlement Lag ............................................................. 51

4.3.3

Performance Options ..................................................... 52

4.3.4

Transaction File Inputs .................................................. 52

4.3.5

Market Data Curves ...................................................... 54

4.3.6

Testing Methodology ..................................................... 55

4.4

Inflation Swap ........................................................................... 55

4.4.1

Notations ..................................................................... 55

4.4.2

Payoff Definitions .......................................................... 56

4.4.3

Pricing Methodology ...................................................... 56

4.4.4

Seasonality Adjustment ................................................. 58

4.4.5

Potential Future Exposure Calculations ............................ 59

4.4.6

Transaction File Inputs .................................................. 60

4.4.7

Market Data Curves ...................................................... 65

4.4.8

Logging Intermediate Results ......................................... 70

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4.5

4.6

4.7

4.8

4.9

5

4.4.9

Testing Methodology ..................................................... 71

Total Return Swap (TRS) ............................................................ 71

4.5.1

Description................................................................... 71

4.5.2

Analytic Price ............................................................... 72

4.5.3

Risky Discount Factors ................................................... 74

4.5.4

Bond Spread Calibration ................................................ 75

4.5.5

Bond Valuation ............................................................. 76

4.5.6

PRICE_TR .................................................................... 76

4.5.7

AI_TR .......................................................................... 76

4.5.8

LIBOR ......................................................................... 77

4.5.9

AI_PREM ...................................................................... 78

4.5.10 LOCKOUT ..................................................................... 78

4.5.11 Transaction File Inputs .................................................. 78

4.5.12 Market Data Curves ...................................................... 88

Constant Maturity (Treasury) Swaps (CMS and CMT) ..................... 91

4.6.1

Pricing Methodology ...................................................... 91

4.6.2

Transaction File Inputs .................................................. 99

4.6.3

Coupon Map Definitions ................................................100

4.6.4

Observables ................................................................108

4.6.5

Market Data Curves .....................................................113

Equity Swap.............................................................................116

4.7.1

Description..................................................................116

4.7.2

Valuing the Equity Leg ..................................................117

4.7.3

Calculating the Forward Equity Price ...............................118

4.7.4

Fixed Index Leg ...........................................................120

4.7.5

IR Leg ........................................................................120

4.7.6

Performance Return Swap .............................................121

4.7.7

Baskets ......................................................................122

4.7.8

Compo Equity Swaps ....................................................122

4.7.9

Instrument Format .......................................................123

4.7.10 Transaction File Inputs .................................................124

4.7.11 Auxiliary Transaction Data File Inputs .............................125

4.6.12 Market Data Curves .....................................................132

4.6.13 Testing Methodology ....................................................137

Bond Repo ...............................................................................137

4.8.1

Description..................................................................137

4.8.2

Transaction File Inputs .................................................138

4.8.3

Testing Methodology ....................................................139

Equity Repo .............................................................................140

4.9.1

Description..................................................................140

4.9.2

Transaction File Inputs .................................................140

4.9.3

Testing Methodology ....................................................142

MODEL SPECIFICATIONS ....................................................................143

5.1

PFE Model for Equity Risk with Jumps ..........................................143

5.1.1

Accounting for Jumps ...................................................143

5.1.2

Alternative Equity Pricing Model .....................................144

5.2

Model Simulation Data Requirements ..........................................147

5.2.1

Market Data CSV file ....................................................147

5.2.2

Model Parameters CSV file ............................................151

5.2.3

External Scenarios CSV File ...........................................155

5.2.4

Stress Testing Data ......................................................156

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5.2.5

6

Input codes .................................................................156

ABBREVIATIONS ................................................................................158

TABLES

Table 1: Document Version History .............................................................. 13

Table 2: PFE and Stress Testing – Definitions Data Requirements .................... 24

Table 3: Instrument Modelling Approach ...................................................... 27

Table 4: QuIC Financial Engineers – Instrument Assignments ......................... 29

Table 5: MultiLeg Map Definiton .................................................................. 30

Table 6: Instrument 1: Model and Solver ..................................................... 30

Table 7: Instrument 1: Transaction File Inputs.............................................. 38

Table 8: EQOptionAmericanExerice Instrument: oSolverPrefs_ information Map 41

Table 9: Sample Yield Data ........................................................................ 44

Table 10: Sample Equity Implied Volatility Data ............................................ 46

Table 11: Sample Dividend Schedule Data.................................................... 47

Table 12: Sample Dividend Yield Data ......................................................... 48

Table 13: Day count Convention Codes ........................................................ 49

Table 14: Instrument 2: Model and Solver.................................................... 50

Table 15: Instrument 2: Transaction File Inputs ............................................ 52

Table 16: Instrument Inflation Swap: Model and Solver ................................. 55

Table 17: Inflation Instrument: Transaction File Inputs .................................. 60

Table 18: Inflation Instrument: Leg Information Map ..................................... 61

Table 19: CouponInflationFixed Map Definition .............................................. 63

Table 20: Inflation Instrument: Observable Map Input ................................... 65

Table 21: Sample Yield Data ....................................................................... 67

Table 22: Sample Yield Data ....................................................................... 68

Table 23: Total Return Swap on a Corporate Bond: Model and Solver .............. 71

Table 24: Generic Instrument: Transaction File Inputs ................................... 78

Table 25: CouponBondTotalReturnSpot Map Definition ................................... 80

Table 26: ObservableBond Map Definition .................................................... 81

Table 27: mpRateSchedule Definition........................................................... 83

Table 28: CouponTRPremSpot Map Definition ............................................... 84

Table 29: LiborObservable Map Definition ..................................................... 86

Table 30: Sample Yield Data ....................................................................... 89

Table 31: Generic Instrument: Transaction File Inputs ................................. 100

Table 32: CouponLibor and CouponCMS Map Definition ................................ 101

Table 33: CouponFixed Map Definition ....................................................... 104

Table 34: Option Payoffs Supported for strOptionType Field .......................... 105

Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map Definition ....... 106

Table 36: ObservableSwapRate Map Definition ............................................ 108

Table 37: ObservableLibor Map Definition ................................................... 111

Table 38: Sample Yield Data ..................................................................... 113

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Table 39: Sample ATM Swaption Volatility Data .......................................... 115

Table 40: Sample Swaption Smile Data ...................................................... 115

Table 41: Instrument 1: Model and Solver .................................................. 116

Table 42: Instrument 1: Transaction File Inputs .......................................... 124

Table 43: EQSwap Instrument: CouponLiborEquityIRLeg Information Map...... 125

Table 44: EQSwap Instrument: CouponFixedEquityIRLeg Information Map ..... 126

Table 45: EQSwap Instrument: IRLeg Information Map: ObservableLiborRate Map

Definition ............................................................................................... 128

Table 46: EQSwap Instrument: CouponTotalReturnEquity Information Map .... 129

Table 47: EQSwap Instrument: EQLeg Information Map: mpEquityObservable

Information Map ..................................................................................... 131

Table 48: Sample Yield Data ..................................................................... 133

Table 49: Sample Dividend Schedule Data.................................................. 135

Table 50: Sample Continuous Dividend Yield Data ....................................... 136

Table 51: Instrument BondRepo : Model and Solver .................................... 137

Table 52: Instrument BondRepo: Transaction File Inputs ............................. 138

Table 53: Instrument EquityRepo: Model and Solver .................................... 140

Table 54: Instrument BondRepo: Transaction File Inputs ............................. 140

Table 55: Sample Yield Data ..................................................................... 149

Table 56: Sample Par Credit Spread Data ................................................... 150

Table 57: Data Type Codes ....................................................................... 151

Table 58: Equity Risk Simulation Model Parameters ..................................... 152

Table 59: External Scenario CSV File’s Rows ............................................... 155

Table 60: Day Count Convention Codes ..................................................... 157

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FIGURES

Figure 1: Sample Yield Curve (CSV Format) .................................................. 44

Figure 2: Sample EquityIndex Curve (CSV Format) ....................................... 45

Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format)............................ 46

Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format) ..................... 47

Figure 5: Sample DividendYield Curve (CSV Format) ..................................... 49

Figure 6: CPI Fixing in PFE Calculations Example ........................................... 60

Figure 7: Sample Yield Curve (CSV Format) .................................................. 67

Figure 8: Sample Yield Curve (CSV Format) .................................................. 68

Figure 9: Sample RealYield Curve (CSV Format)............................................ 69

Figure 10: Sample HistoricalInflationIndex Curve (CSV Format) ...................... 69

Figure 11: DerivedInflationIndex Curve (CSV Format) ................................... 70

Figure 12: Sample InflationSeasonality Curve (CSV Format) ........................... 70

Figure 13: Bond Spread Calibration ............................................................. 75

Figure 14: Accrued Interest Example ........................................................... 77

Figure 15: Accrued Interest Example ........................................................... 77

Figure 16: Example of Generic Transaction Input for TRSB ............................. 79

Figure 17: Example of TRLegInfo Map Inputs ................................................ 81

Figure 18: Example of BondObservable Map Inputs ....................................... 83

Figure 19: Example of RateScheduleMap Inputs ............................................ 83

Figure 20: Example of CouponTRPremSpot Map Inputs .................................. 86

Figure 21: Examples of LIBOR Map Inputs .................................................... 88

Figure 22: Sample Yield Curve (CSV Format) ................................................ 89

Figure 23: Par Credit Spread Curve ............................................................. 91

Figure 24: Generic Configuration of a Single Cash Flow Based on a Swap Rate . 91

Figure 25: Caplet and Floorlet Payoff ........................................................... 93

Figure 26: j-th Coupon In-Advance.............................................................. 98

Figure 27: j-th Coupon In-Arrears ............................................................... 98

Figure 28: Sample Yield Curve (CSV Format) .............................................. 114

Figure 29: Sample EquityImpliedVolMtx Curve (CSV Format) ........................ 115

Figure 30: Sample EquityImpliedVolMtx Curve (CSV Format) ........................ 116

Figure 31: Sample Yield Curve (CSV Format) .............................................. 134

Figure 32: Sample EquityIndex Curve (CSV Format) .................................... 134

Figure 33: Sample DiscreteAbsoluteDividend Curve (CSV Format) ................. 135

Figure 34: Sample ContinuousDividendYield Curve (CSV Format) .................. 137

Figure 35: Sample Exchange Curve (CSV Format) ....................................... 148

Figure 36: Sample Yield Curve (CSV Format) .............................................. 149

Figure 37: Sample ParCreditSpread Curve (CSV Format) .............................. 150

Figure 38: Sample EquityIndex Curve (CSV Format) .................................... 151

Figure 39: Sample Equity Index Simulation Model Parameters ...................... 155

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EQUATIONS

Equation 1 – Equity Risk Simulation............................................................. 22

Equation 2 – Equity Options ....................................................................... 30

Equation 3 – Equity Options ....................................................................... 31

Equation 4 – Equity Options ....................................................................... 31

Equation 5 – Equity Options ....................................................................... 31

Equation 6 – Equity Options ....................................................................... 32

Equation 7 – Equity Options ....................................................................... 33

Equation 8 – Equity Options ....................................................................... 33

Equation 9 – Equity Options ....................................................................... 34

Equation 10 – Equity Options ...................................................................... 34

Equation 11 – Equity Options ...................................................................... 35

Equation 12 – Equity Options ...................................................................... 35

Equation 13 – Equity Options ...................................................................... 36

Equation 14 – Equity Options ...................................................................... 36

Equation 15 – Equity Options ...................................................................... 36

Equation 16 – Equity Options ...................................................................... 36

Equation 17 – Equity Options ...................................................................... 37

Equation 18 – Equity Options ...................................................................... 37

Equation 19 – Equity Options ...................................................................... 50

Equation 20 – Equity Options ...................................................................... 50

Equation 21 – Equity Options ...................................................................... 50

Equation 22 – Equity Options ...................................................................... 50

Equation 23 – Equity Options ...................................................................... 51

Equation 24 – Equity Options ...................................................................... 51

Equation 25 – Equity Options ...................................................................... 51

Equation 26 – Equity Options ...................................................................... 51

Equation 27 – Inflation Swaps .................................................................... 56

Equation 28 – Inflation Swaps .................................................................... 56

Equation 29 – Inflation Swaps .................................................................... 56

Equation 30 – Inflation Swaps .................................................................... 56

Equation 31 – Inflation Swaps .................................................................... 57

Equation 32 – Inflation Swaps .................................................................... 57

Equation 33 – Inflation Swaps .................................................................... 57

Equation 34 – Inflation Swaps .................................................................... 57

Equation 35 – Inflation Swaps .................................................................... 57

Equation 36 – Inflation Swaps .................................................................... 58

Equation 37 – Inflation Swaps .................................................................... 58

Equation 38 – Inflation Swaps .................................................................... 58

Equation 39 – Inflation Swaps .................................................................... 59

Equation 40 – Inflation Swaps .................................................................... 59

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Equation 41 – Total Return Swap ................................................................ 72

Equation 42 – Total Return Swap ................................................................ 74

Equation 43 – Total Return Swap ................................................................ 75

Equation 44 – Total Return Swap ................................................................ 76

Equation 45 – Total Return Swap ................................................................ 76

Equation 46 – Total Return Swap ................................................................ 77

Equation 47 – Total Return Swap ................................................................ 77

Equation 48 – Total Return Swap ................................................................ 78

Equation 49 – Total Return Swap ................................................................ 78

Equation 50 – CMS and CMT ....................................................................... 92

Equation 51 – CMS and CMT ....................................................................... 92

Equation 52 – CMS and CMT ....................................................................... 93

Equation 53 – CMS and CMT ....................................................................... 94

Equation 54 – CMS and CMT ....................................................................... 94

Equation 55 – CMS and CMT ....................................................................... 94

Equation 56 – CMS and CMT ....................................................................... 94

Equation 57 – CMS and CMT ....................................................................... 95

Equation 58 – CMS and CMT ....................................................................... 95

Equation 59 – CMS and CMT ....................................................................... 95

Equation 60 – CMS and CMT ....................................................................... 95

Equation 61 – CMS and CMT ....................................................................... 95

Equation 62 – CMS and CMT ....................................................................... 96

Equation 63 – CMS and CMT ....................................................................... 96

Equation 64 – CMS and CMT ....................................................................... 96

Equation 65 – CMS and CMT ....................................................................... 97

Equation 66 – CMS and CMT ....................................................................... 97

Equation 67 – CMS and CMT ....................................................................... 97

Equation 68 – CMS and CMT ....................................................................... 97

Equation 69 – Equity Swap ....................................................................... 117

Equation 70 – Equity Swap ....................................................................... 118

Equation 71 – Equity Swap ....................................................................... 118

Equation 72 – Equity Swap ....................................................................... 118

Equation 73 – Equity Swap ....................................................................... 119

Equation 74 – Equity Swap ....................................................................... 119

Equation 75 – Equity Swap ....................................................................... 119

Equation 76 – Equity Swap ....................................................................... 120

Equation 77 – Equity Swap ....................................................................... 120

Equation 78 – Equity Swap ....................................................................... 120

Equation 79 – Equity Swap ....................................................................... 121

Equation 80 – Equity Swap ....................................................................... 121

Equation 81 – Equity Swap ....................................................................... 122

Equation 82 – Equity Swap ....................................................................... 122

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Equation 83 – Equity Swap ....................................................................... 122

Equation 84 – Equity Swap ....................................................................... 122

Equation 85 – Equity Swap ....................................................................... 123

Equation 86 – Equity Swap ....................................................................... 123

Equation 87 – Model Specifications ............................................................ 143

Equation 88 – Model Specifications ............................................................ 144

Equation 89 – Model Specifications ............................................................ 144

Equation 90 – Model Specifications ............................................................ 145

Equation 91 – Model Specifications ............................................................ 145

Equation 92 – Model Specifications ............................................................ 145

Equation 93 – Model Specifications ............................................................ 145

Equation 94 – Model Specifications ............................................................ 145

Equation 95 – Model Specifications ............................................................ 145

Equation 96 – Model Specifications ............................................................ 146

Equation 97 – Model Specifications ............................................................ 146

Equation 98 – Model Specifications ............................................................ 146

Equation 99 – Model Specifications ............................................................ 147

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1

INTRODUCTION

1.1

Purpose of This Document

This document provides detailed specifications of the risk-factor scenariogeneration models and financial instruments that are to be added to HSBC’s

counterparty credit exposure calculations. For a description of the requirements

on which these specifications are based, see the document ‘QuIC Response to

HSBC Credit Risk New Products RFP’.

This is a working document, owned by QuIC, which will evolve throughout the

discovery phase of the workstream 2 (‘WS2’) project.

Chapter 4 Instrument Specifications, starting on page 30, has a section per

financial instrument, explaining the financial model and its variables, and the

parameterization within QuIC Script. Each instrument-specific section will be

signed off by both HSBC (TMR) and QuIC incrementally, to allow the staggered

development and delivery of each product by the QuIC Financial Engineering

team in Vancouver.

1.2

Document Audience

This document is for:

Callum Wingrove, HSBC Project Team, TMR team

QuIC’s project team, financial engineers and QuIC Script programmers.

1.3

Where to Go for Help

For additional help with information covered in this document, contact:

Jay Rao, Project Manager

+44 20 7743 6325 (O)

+44 7852434033 (M)

Email: jay.rao@quic.com

Alternatively call the QuIC customer service at 1.877.689.1888 within North

America, or 1.306.337.1446 outside North America.

Technical support is also available by email at techsupport@quic.com.

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1.4

Document Version History

The following table (Table 1: Document Version History) shows changes made to

this document from V2.14 onwards:

Table 1: Document Version History

Version

Updated by

Change Description

2.14

Julian Maynard-Smith,

Technical Author

General literary edit (correcting typos, simplifying descriptions,

etc).

Added ‘Document Version History’ section.

Changed appendices to chapters, to address heading

numbering problems when pasting instrument-specific

information from other documents.

Added 5.2 Model Simulation Data Requirements, starting on

page 147.

Added new version of the CMS document (‘HSBC CMS

specification 1.5’).

Added new versions of the American Exercise Vanilla Equity

Option, and European Exercise Vanilla Equity Option, sections

(Equity Option Instrument Specification v5).

2.15

Julian Maynard-Smith,

Technical Author

Added new section, 4.7 Equity Swap, starting on page 116.

2.16

Julian Maynard-Smith,

Technical Author

Changes requested by Horst for sign-off on the equity/credit

simulation model. All the changes are in section 3.1 PFE

Simulation, starting on page 22:

The equation in 3.1.1 Equity Risk Simulation on page 22

adjusted so that there is no factor

term

Fn

multiplying the drift

n .

Table 2 (page 24): For the first row of the table, Risk factor n

at time tj under scenario i , the text in the two Data

Requirements columns has been adjusted to mention Calypso

as well as Sophis.

Table 2 (page 24): For the sixth row of the table, Trigger time

step, the word ‘stress’ has been removed from the sentence:

‘The trigger time step is defined in the scenario set.’

New section added, 3.1.3 Jumps, starting on page 26.

Also, removed the tables in Chapter 2 Sign-Offs, on page 21,

since this information is already captured in both the weekly

project status reports and the instrument build matrix. In its

place, there is a description of where the weekly project status

reports are stored.

2.17

Julian Maynard-Smith,

Technical Author

Added new versions of American and European Exercise Vanilla

Options.

The sections come from Equity Option Instrument

Specification_v6, and include descriptions on physically settled

options and a delay for cash-settled American options.

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Version

Updated by

Change Description

2.18

Julian Maynard-Smith,

Technical Author

Added new section for the benefit of HSBC staff: 3.4 QuiC

Financial Engineers per Instrument / Model, on page 29.

Added new versions of American and European Exercise Vanilla

Options. The sections come from Equity Option Instrument

Specification_v7, the changes for which are as follows:

“Cleaned up definition of forward equity prices for dividend

calculations. Changed value of physically settled options on

exposure dates within the settlement lag to be the value of the

forward contract, strike being exchanged for the equity on the

settlement date.” (Allan Cowan, QuiC financial engineer)

2.19

Julian Maynard-Smith,

Technical Author

Added new versions of American and European Exercise Vanilla

Options, from Equity Option Instrument Specification_v7:

contain major modifications to the formulation of physically

settled options.

Fixed some formatting bugs in the document.

2.20

Julian Maynard-Smith,

Technical Author

Replaced the existing section 5.2 Model Simulation Data

Requirements, starting on page 147, with ‘Equity Risk

Simulation Model Data Requirements’ as written by David

Orford, Technical Author.

2.21

Julian Maynard-Smith,

Technical Author

Added new versions of American and European Exercise Vanilla

Options, from Equity Option Instrument Specification_v9. The

new sections contain new dividend and physical settlement

descriptions.

2.22

Julian Maynard-Smith,

Technical Author

CMS/CMT section: removed a number of redundant sections.

Julian Maynard-Smith,

Technical Author

New sections for American/European-exercise equity options:

updates to describe how the settlement lag will be specified (as

clarified in an email from John Ballaram).

2.23

Changes related to equity options:

Removed references to baskets for equity options, as they have

been removed from the project scope. Note that baskets for

equity swaps and total-return swaps are still in scope.

Added new versions of equity option sections (from Equity

Option Specification_v10): daycount and compounding

attributes added to the definition of the dividend yield curve.

Added further changes to the American/Equity Option sections,

affect equations 2.8 and 2.9 and the surrounding text and

equations 3.7 and 3.8 and the surrounding text.

Source document: Equity Option Instrument Specification_v12,

written by Allan Cowan.

2.24

Julian Maynard-Smith

New Equity Swap section, taken from v4 of the Equity Swap

specification, written by Allan Cowan, who describes the

changes as follows:

Updated description of forward price calculation to be consistent

with equity derivative spec. Introduced dividend ratio

parameter to unify description of total return and price return

swaps - this resulted in significant changes to the document

format. Split IR leg into a separate Fixed and Floating leg map

in the input file.

2.25

Kirstie Wilson

New Total Return Swap section, from TRS Instrument

Specification (V1.4), written by Jeff Hawkins.

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Change Description

2.26

Kirstie Wilson

New Equity Option section from v13 of the Equity Option

Instrument Specification by Allan Cowan to include:

A description of the performance option and how we will value

it, and relevant changes to the instrument inputs.

Further details about the user settings available to set

preferences in the FD solver.

2.27

Jay Rao

Updated TRS specifications from Jeff Hawkins. This document

defines the pricing methodology in details as per the latest

discussions between Jeff and Dong –

Bonds are valued using a risky discount factor which is

based on swap yield curve, CDS spreads and a basis

adjustment (this needs further definition)

Data inputs

Minor notational changes

2.28

Jeff Hawkins

Minor changes to TRS specifications in line with discussions with

Horst

2.29

Jay Rao

Equity Swaps

Changes to sections – Baskets, Quanto

Additions to Table 33: EQSwap instrument: EQLeg information map – Field

apFXInfo

Table 31: EQSwap instrument: IRFixedLeg information map –

field pFXInfo

Equity Options – Performance Options

Performance option section has the notation changes

as suggested in an email.

Minor changes to reflect the comments from Thomas

in the attached email – adding a nominal amount that

is separate from the number of shares input.

Added a FX curve, this will be needed so that all option

prices in a portfolio are converted to a common

currency for reporting PFE

2.36

Allan Cowan

Equity Swaps

Updating with v8 of the equity swap spec: Fixed a few

typos, and clarified that apFXUnderlying will be a FX rate from

equity currency to USD.

TRS

Updated pricing methodology and data inputs to make a clearer

distinction of bond currency, TR currency, and reporting

currency.

Updated description of the credit spread curve market data

type in the TRS section

Jeff Hawkins

2.37

Jeff Hawkins

TRS

Updated data inputs and to allow for a different funding leg

currency and funding riskless discount factors.

Updated exchange rates so they all convert to the reporting

currency.

2.38

Jeff Hawkins

TRS

Updated some the bond return so that the previous bond price

is converted at what was the FX spot rate at the time.

Updated the MTM of Lockout coupons to be discounted by

riskless discount factor.

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Updated by

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2.39

Bernadette McGovern,

Technical Author

Inflation Swaps

Added Inflation Swaps section from Inflation Swap Specification

V1 originated by Curtis Sam. The input and testing

requirements for Inflation zero coupon and year on year swap

are specified here.

General

Edited this HSBC Instrument Specifications document from

general formatting, typos and consistency perspective – and

specifically:

Spelling errors.

Wrong numbering of tables ie the captions have been

typed manually therefore the numbering was not

updated.

Inconsistency as regards use of Initial Capital in

headings.

References are to page numbers and sections - which,

shouldn't be done because if anything shifts, it creates

an issue. Replacing them with hyperlinked references

to the section number and name.

Incorrect use of styles resulting in 'Error' messages

and not the actual content in a table.

"<>" left in several places, instead of it being replaced

with actual text.

References to documents but not the actual location of

them or how to get them.

Inconsistent use of styles for "Example" – and

sometimes numbered – also the example name not

put in full, so too vague.

Some sections badly numbered and manually typed –

this affected the numbering in the whole document.

The automatic fields for the version number were

overwritten manually.

Tables not formatted consistently or the paragraph

spacing.

Additional editing to be done to correct more of these items.

2.40

Section 3.2.2 Inflation added to 3 Project Scope.

Section 3.3 Financial Instruments of 3 Project Scope – removed

the third and fourth rows in the inflation section ie the hybrid

and inflation-linked bonds are not in scope. Changed "JY

Model" to "Arbitrage free".

Awaiting responses on some reference queries see “<hold…>”,

which will be put in next draft.

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Bernadette McGovern,

Technical Author

Inflation Swaps

4.4.2 Payoff Definitions of 4 Instrument Specifications edited to

add paragraph regarding leverage factor and spread.

4.4.6.4.1 Example – Inflation Leg Observable Map Input – third

line of amended.

4.4.7.2 Nominal Yield Curve – changes to variable attributes.

4.4.7.4 Real Yield Curve – changes to variable attributes.

Example changed.

4.4.7.5 Historical Inflation Index Curve – change to title of

Figure.

4.4.7.6 Spot Inflation Index Curve – change to format and

additional description of curve, updated to Figure to reflect this.

4.4.7.7 Inflation Seasonality Curve – change to curve format

and sample in the Figure.

4.4.8 Logging Intermediate Results – new section added.

Equity Options

4.2.1 Description – paragraphs added “Early exercise of a

scenario… used in the equation (2.5).”

4.2.1.1 Cash Settled Options – equations renumbered through

to the end of entire Equity Options section. Text changes in the

last two paragraphs.

4.2.1.2 Physically Settled Options – equation change made.

Last paragraph removed.

4.2.7 Definition of Daycounts – new section added.

The word ‘Exercise’ has been removed from each instrument

name.

Total Return Swap

New section added – 4.5.4 Bond Spread Calibration. 4.5.5 Bond

Valuation updated.

Figures in Figure 13: Bond Spread Calibration and Figure 14:

Accrued Interest Example replaced.

CMS/CMT

New section added – 4.1 Cross Instrument Inputs

Map Inputs: MultiLeg.

General Updates

All equations numbered and referenced where necessary. Table

of contents put in for Equations, Figures and Tables. General

editing as regards formatting. Some obsolete references to

Appendices removed.

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2.42

Bernadette McGovern,

Technical Author

Inflation Swaps

4.4.3 Pricing Methodology edited to add paragraph regarding

ST_MONTH and OATI prior to Equation 37 – Inflation Swaps,

where the equation has also been changed. Equation 38 –

Inflation Swaps – the equation has been changed, line

regarding PFE calculation added in the subsequent paragraph.

4.4.5 Potential Future Exposure Calculations edited to add

paragraph regarding CPI reference month.

4.4.6.3 Map Inputs: CouponInflationFixed entire section edited.

4.4.7.6 Spot Inflation Index Curve – line added about ‘historical

index fixing’ added.

Equity Swaps

4.7.9 Instrument Format – first paragraph edited to reword

sentence about LIBOR.

4.7.10 Transaction File Inputs, Table 42: Instrument 1:

Transaction File Inputs – constraints column content edited and

the subsequent sample transaction line.

4.7.11 Auxiliary Transaction Data File Inputs – several general

edits eg input names and formats throughout the section and in

the following sections –

4.7.11.1 CouponLiborEquityIRLeg Data Structure, 4.7.11.2

CouponFixedEquityIRLeg Data Structure, 4.7.11.3

mpObservable Structure of CouponLiborEquityIRLeg Map,

4.7.11.9 Dividend Yield Curve – the word 'continuous' removed

from 'ContinuousDividendYield' curve.

CMS/CMT

4.6.2 Transaction File Inputs – Example Entry changed, Table

31: Generic Instrument: Transaction File Inputs – Constraint

updated for Field 2.

4.6.3.2 Floating Leg Map Inputs: CouponLibor and CouponCMS

– title changed from '.. CouponFloat'. Table 32: CouponLibor

and CouponCMS Map Definition – Map Key and Type Code

changed for Daycount convention, constraint changed for

mpObservable, arPastFixing changed from arPastReset and

constraint changed. 4.6.3.2.1 Examples Map Key references

changed.

4.6.3.3 Map Inputs: CouponFixed, Table 33: CouponFixed Map

Definition – strDaycount put in and 4.6.3.3.1 Examples

updated.

4.6.3.4 Cap/Floor Map Inputs: CouponLiborCapFloor and

CouponCMSCapFloor – title changed from '…CouponCap Floor'.

Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map

Definition – strDaycount put in, mpObservable constraint

changed, arPastFixing put in, bUseMoneyness added. 4.6.3.4.1

Examples – Map Key names updated and bUseMoneyness

added. Table 37: ObservableLibor Map Definition –

'pHistoricalRate put in and last row pVol updated.

4.6.4.1 Map Inputs: ObservableSwapRate, Table 36:

ObservableSwapRate Map Definition – last 2 rows updated,

4.6.4.1.1 Example: 5 Year, Semi-Annual Swap Rates –

updated.

4.6.4.2 Map Inputs: ObservableLibor – title changed and Table

37: ObservableLibor Map Definition. 4.6.4.2.1 Examples – Map

Key name updated.

4.5.4.3 Map Inputs: ObservableBond – section removed. 4.6.5

Market Data Curves – whole new section added.

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Bernadette McGovern,

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Total Return Swap

4.5.11 Transaction File Inputs, Table 24: Generic Instrument:

Transaction File Inputs – changed instrument name from 'TRSB'

to 'LegFrameGeneric' because it uses the LegFrameGeneric

input structure. Field No. 3 updated. Figure 16: Example of

Generic Transaction Input for TRSB – all updated.

4.5.11.2 Map Inputs: CouponBondTotalReturnSpot – updated.

Table 25: CouponBondTotalReturnSpot Map Definition –

stryType is changed from 'TRBondLeg' to

'CouponBondTotalReturnSpot' to be more specific - this is just a

user input, not a data item, Map key changed from

mpBondObservable to mpObservable - this is a user input, not

a data item. Map key changed from 'pFXBondInfo' to

'pExchangeBond'. This is a user input, not a data item. Figure

17: Example of TRLegInfo Map Inputs – updated.

4.5.11.3 Map Inputs: ObservableBond – updated. Table 26:

ObservableBond Map Definition – the method for describing

bond coupon dates has been changed from supplying adjusted

dates (adtStart, adtEnd) to supplying dtSettle, dtMaturity,

dtFirstPayment, strPayFreq. This is an additional map that

allows for reuse of schedules. Figure 18: Example of

BondObservable Map Inputs – all updated.

4.5.11.4 Map Inputs: mpRateSchedule – updated. The standard

bond input calls for a single fixed rate, single notinoal amount

and single leverage. If these inputs vary by coupon then a rate

schedule map must be used.

4.5.11.5 Map Inputs: CouponTRPremSpot – updated. Table 28:

CouponTRPremSpot Map Definition – name change from

‘TRFundingLeg’ to ‘CouponTRPremSpot’. Daycount required for

calculating accrued interest. Figure 20: Example of

CouponTRPremSpot Map Inputs – all updated.

Error! Reference source not found. Error! Reference

source not found. – a map describing the lockout features has

been added (the previous method had these inputs in the

funding leg description).

4.5.11.6 Map Inputs: LiborObservable – updated. Table 29:

LiborObservable Map Definition – first row updated, the strType

value changed from 'ObservableLibor' to 'LiborObservable'.

Figure 21: Examples of LIBOR Map Inputs – all updated.

2.44

Equity Swaps

4.7.2 Valuing the Equity Leg – sentence added "We allow for a

lag…".

4.7.9 Instrument Format – sentence edited "For an equity

leg..".

4.7.11.4 CouponTotalReturnEquity Data Structure, Table 46:

EQSwap Instrument: CouponTotalReturnEquity Information

Map – Map Key 'adtEnd' description edited, Map key

'adtpayment' added. 4.7.11.4.1 Example – 'adtPayment…' row

added.

More detail added to reasons for updates in 2.43 updates to

TRS.

2.45

Inflation Swaps

4.4.6 Transaction File Inputs, 4.4.6.2 Map Inputs:

CouponInflation, Table 18: Inflation Instrument: Leg

Information Map – May Key 'strDaycount' and Type Code 'S'

added.

4.1 Cross Instrument Inputs, 4.1.1 Map Inputs: MultiLegTable

5: MultiLeg Map Definiton – Map Key 'strType' and Type Code

'S', Map Key 'ampLegs' and Type Code 'AL' added, table moved

to common area within Instrument section.

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CMS/CMT

4.6.3.2 Floating Leg Map Inputs: CouponLibor and CouponCMS,

Table 32: CouponLibor and CouponCMS Map Definition – Title

changd, Constraint for 'strType' changed to 'CouponLibor or

CouponCMS'.

4.6.3.4 Cap/Floor Map Inputs: CouponLiborCapFloor and

CouponCMSCapFloor,

Table 35: CouponLiobrCapFloor and CouponCMSCapFloor Map

Definition – Title changed, Constraint for 'strType' changed to

'CouponLiobrCapFloor or CouponCMSCapFloor', Constraint for

'mpObservable' changed to 'CouponLiobrCapFloor or

CouponCMSCapFloor, Constraint for 'arPastFixing' changed to

'Optional – if omitted, uses the underlying’s pHistoricalRate'.

2.47

TRS

4.5 Total Return Swap (TRS) - Entire section replaced.

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2

SIGN-OFFS

Before QuIC Script development on a specific simulation model or instrument can

start, both HSBC and QuIC must sign off the specification.

The latest sign-off status per simulation model and instrument is available in the

latest HSBC Project Status Report, available in the following locations:

For HSBC personnel, the Lotus Notes team room entitled ‘Credit Risk new

Products Programme’

For QuIC personnel, the QuIC portal at: http://tinyurl.com/2m54vs.

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3

PROJECT SCOPE

3.1

PFE Simulation

The key risk factors to be simulated are equity prices and five-year par credit

spreads1. Risk factors specific to FX rates, interest rates, and inflation trades will

be provided via external scenarios.

3.1.1

Equity Risk Simulation

Both equity prices and five-year par spreads will be simulated as follows:

Equation 1 – Equity Risk Simulation

F 2

n n n t j t j 1

2

S in t j S in t j 1 At j exp

Bt j

F

nxyz z i (t j 1 , t j ) xyz Fn ni (t j ) t j t j 1

n xyz {Market

Driver Indices}

Here ‘n’ indexes the risk factor (be it an equity price or a par spread), ‘i’ indexes

the scenario, and ‘j’ indexes the time step. This model extends the existing HSBC

credit spread model in the following respects:

There is a risk factor-specific drift rate n

There is a new term

nequity index z i (t j 1 , t j ) equity index

arising from contributions

from an equity index

The idiosyncratic shocks n may be correlated.

The existing HSBC credit-spread model handles three market driver indices:

region, sector and rating. In principle, the current model will support an

additional equity index. Please note that users can change the number of market

driver indices. The idiosyncratic shocks n are correlated

N (0, n2 ) -distributed

random variables independent of the market drivers. The parameters A, B, and Fn

are used for stress testing.

1

The benchmark spread is a five-year par spread. This is to be consistent with HSBC’s existing QuIC

implementation for CDS/CDX PFE calculations.

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HSBC will explicitly specify pairwise correlations for an arbitrary (but typically

small) subset of idiosyncratic shock pairs. For all pairs where a correlation is

unspecified, a correlation of zero will be assumed. Consequently, the correlation

matrix of the idiosyncratic components will have a block structure, where risk

factors that have been assigned nonzero correlations are put in one block with

correlation matrix C, and all other risk factors are put in another block with a

correlation matrix equal to the identity. To generate idiosyncratic shocks, PCA will

be applied to C to obtain a square-root representation C

terms will then be simulated via the equation

(1)

U

0

(N )

UU T . The idiosyncratic

(1)

0

I

( N )

where is a permutation taking the correlated components into the first block.

The ns are uncorrelated

N (0, n2 ) random variables.

The market-driver indices in Equation 1 – Equity Risk will be provided to QuIC in

the form of external scenarios having the same format as the existing creditspread model. HSBC will specify all model parameters as inputs. QuIC will

generate idiosyncratic shocks and use Equation 1 – Equity Risk to create

scenarios for equity prices and credit spreads.

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Table 2: PFE and Stress Testing – Definitions Data Requirements

Notation

Definition

Data Requirements

PFE

Stress Testing

Risk factor n at time tj under scenario i.

Initial values will be passed in from Calypso for

credit spreads and from Sophis for equity spot

prices.

Initial values will be passed in from Calypso for

credit spreads and from Sophis for equity spot

prices.

Time-varying parameter used for applying relative

stress changes. Unless explicitly specified, this

parameter has a default value of 1.

Will not be passed in, and should take on its

default value of 1 at all time steps.

May be passed in by Scenario Modulator, but

should otherwise take on its default value of 1 at

all time steps.

Btj

Time-varying parameter used for applying absolute

stress changes. Unless explicitly specified, this

parameter has a default value of 0.

May be passed in by Scenario Modulator, but

should otherwise take on its default value of 0 at

all time steps

May be passed in by Scenario Modulator, but

should otherwise take on its default value of 0 at

all time steps.

n , n

Annualised volatility, annualised drift rate.

May be passed in by Scenario Modulator, but

should otherwise be obtained from data file output

from the regression tool.

May be passed in by Scenario Modulator, but

should otherwise be obtained from data file output

from the regression tool.

Fn

Volatility scaling factor obtained through a backtesting algorithm.

Will be provided to QuIC as a data file output from

the regression tool.

Will be provided to QuIC as a data file output from

the regression tool.

tj

Trigger time step.

Defined in the scenario set.

Defined in the scenario set.

nxyz

Beta (or regression coefficient) of risk factor n,

relative to market index xyz. Typically obtained

through standard multi-factor regression analysis.

Will be provided to QuIC as a data file output from

the regression tool.

Will be provided to QuIC as a data file output from

the regression tool.

Si t j

n

Atj

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Notation

Definition

Data Requirements

PFE

z i (t j 1 , t j ) xyz

Log-return scenario for a market index between tj-1

and tj, for scenario path i. ASE provide scenario

data in the form

computes

ni (t j )

i

i

z (0, t j )

z (t j 1 , t j )

xyz

xyz

from which QuIC

.

Idiosyncratic random return, drawn from a normal

distribution with zero mean and standard deviation

n.

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Stress Testing

Will be passed in by Scenario Modulator in the

form z

i

(0, t j ) xyz . Must be converted to

Will be passed in by Scenario Modulator in the

form z

i

(0, t j ) xyz . Must be converted to

z i (t j 1 , t j ) xyz by subtracting

z i (t j 1 , t j ) xyz by subtracting

z i (0, t j 1 ) xyz from z i (0, t j ) xyz .

z i (0, t j 1 ) xyz from z i (0, t j ) xyz .

Must be drawn by QuIC for each issuer (ie not per

contract or per trade) and output to a file under

each scenario and time step for each issuer.

Must be drawn by QuIC for each issuer (ie not per

contract or per trade) and output to a file under

each scenario and time step for each issuer.

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3.1.2

Credit Spread Simulation

Like the existing credit spread simulation model used for HSBC’s CDS/CDX

portfolio, the initial term structure of credit spreads will be bootstrapped from the

initial par spread curve. Simulated future simulated credit spread term structures

will be based on this initial term structure and the simulated five-year par spread.

Thus, on any PFE simulation date, the full term structure of credit spreads (the

‘spread curve’) can be recovered. For pricing simple instruments like CDSs or

CDXs, the stochastic nature of credit spreads is irrelevant in that we can price

these instruments ‘off the spread curve’ at any time step in any PFE simulation.

To calculate a CDS price, we need not know anything about the volatility of the

credit spread eg we only need to know the simulated spread curve.

3.1.3

Jumps

Equity spot prices and credit spreads exhibit jump returns, which can have a

material impact on PFE. Such jumps will not be in scope for the initial release of

the simulation model. Where required, the simulation will be adjusted for the

effects of jumps through the volatility-scaling factors Fn .

3.1.4

Default

Another aspect of the PFE simulation process is the simulation of default by

individual equities. This requires that we make a link between credit spreads and

default probabilities – we must ensure that default is more probable when credit

spreads are high.

Note: The simulation of defaults is not part of the initial release.

3.1.5

Basket

As equity swaps of a basket are in scope they will be simulated by individually

simulating each stock in the basket and summing to find the return of the basket.

Dividends yields will be provided for each name in the basket to be used as with

the equity options.

3.2

3.2.1

Pricing Models

Equity

Equity derivatives will be priced using the Black-Scholes model. Given a simulated

equity price at any time step of a given PFE scenario, a Black-Scholes volatility

will be looked up from an input volatility surface, indexed by time-to-maturity and

option moneyness. The option will then be priced based on this volatility. For the

sake of consistency with front-office methodology, credit spreads will not be

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accounted for in equity option pricing.2 For the same reason, a combination of

dividend types will be supported. A time-indexed array of explicit dividends up to

a certain date, followed by a continuous dividend yield, will be supported. Explicit

dividends may either be expressed in absolute (eg dollar amount) terms, or in

relative (eg proportion of stock price) terms.

3.2.2

Inflation

Zero coupon inflation swap and year-on-year inflation swap are supported.

Features such as arbitrary index lag and payment frequency are allowed, as well

as leverage factor and spread. They are priced with the nominal and real yield

curves with the consideration of the seasonality adjustment's term structure of

the inflation index. The convexity adjustment due to the payment lag is assumed

to be small and therefore neglected. For PFE calculations, the inflation index is

not treated as a primary risk factor, but is driven by the nominal and real yield

curves and is taken to assume the expected forward index value, viewing from

the last PFE date.

3.3

Financial Instruments

Financial instruments within the scope of WS1 are:

Table 3: Instrument Modelling Approach

2

No.

Instrument

Type

Exists

(Y/N/

Proto)

Instrument

Features

Pricing

Model

Solver

QuIC

Name

1

Vanilla

Equity

Derivatives

Yes

Call / Put

(American)

BlackScholes

Finite

Difference

EQ:

Option

Vanilla

American

Comments

For equity options subject to default risk, this approach is somewhat more controversial since

textbook pricing methods only allow us to “price off the curve” if the curve is deterministic.

However, the model calibration and computation involved in a fully rigorous treatment of stochastic

credit spreads is highly complex; and the exposure contribution of an equity option is far more

sensitive to the underlying equity price than it is to the credit spread. Therefore we choose to make

the following modeling compromise: when calculating the exposure of equity options, the option

pricer will assume that the simulated equity spread at any given time step, in any given PFE

scenario, is deterministic for the remainder of the option’s lifetime, despite the fact that at the next

PFE time step the entire spread curve will be subject to a stochastic shock. An alternative two-factor

methodology, in which spreads are driven by a CIR square-root default intensity process, is also

conceivable. However, the attendant model calibration challenges are substantial since they require

a parameter-freezing technique (cf. Piterbarg (2005), Risk Magazine) and the numerical inversion of

two complex characteristic functions (cf. Bakshi et al (1997), Journal of Finance). Moreover, it is not

clear how to capture reasonable volatility surface behaviour with this type of model without

introducing a third stochastic volatility state variable (Bakshi et al (1997)). The attendant model

dimensionality issues rule out this approach for large-scale PFE calculations.

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No.

2

3

4

Instrument

Type

Inflation

Swap (with

leverage

and lag)

Inflation

Swap

Instrument

Features

Pricing

Model

Solver

QuIC

Name

Yes

Call / Put

(European)

BlackScholes

Analytic

EQ:

Option

Vanilla

European

No

Zero

Coupon

Arbitrage

Free

Analytic

No

Year-onYear

Arbitrage

Free

Analytic

TRS

Proto

Single Name

Arbitrage

Free

Analytic

TRS

Proto

Basket

Arbitrage

Free

Analytic

Yes

Vanilla

Swap

Linear

Swap

Rate

Analytic

No

Caps/Floors

Linear

Swap

Rate

Analytic

approximation

No

Digitals

Linear

Swap

Rate

Analytic

approximation

No

Swaptions

Linear

Swap

Rate

Analytic

approximation

Yes

Vanilla

Swap

Linear

Swap

Rate

Analytic

No

Caps/Floors

Linear

Swap

Rate

Analytic

approximation

No

Digitals

Linear

Swap

Rate

Analytic

approximation

No

Swaptions

Linear

Swap

Rate

Analytic

approximation

No

PRS

(dividend

not

included)

Arbitrage

Free

Analytic

CMS (inarrears and

in-advance)

CMT (inarrears and

in-advance)

5

Exists

(Y/N/

Proto)

Non-callable

Equity

(Index)

Swap

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Comments

CMS

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No.

6

Instrument

Type

Repo

3.4

Exists

(Y/N/

Proto)

Instrument

Features

Pricing

Model

Solver

No

TRS

(dividend

included)

Arbitrage

Free

Analytic

No

PS (either

leg could be

PRS or TRS

or both)

Arbitrage

Free

Analytic

No

Govt

Underlying

Arbitrage

Free

Analytic

No

Corporate

Underlying

Arbitrage

Free

Analytic

No

Equity

Underlying

Arbitrage

Free

Analytic

QuIC

Name

Comments

QuiC Financial Engineers per Instrument / Model

The following table (Table 4: QuIC Financial Engineers – Instrument Assignments)

shows which QuIC financial engineer is assigned to which instrument or

simulation model. The QuIC FE is responsible both for developing the software

and for writing the specification (see relevant section in Chapter 4 Instrument

Specifications.

Note:

See CRISP New Products Testing Strategy V0.3 (located in the

HSBC Credit Risk New Products Programme Lotus Notes work

space and QFT Instrument Testing.

Table 4: QuIC Financial Engineers – Instrument Assignments

Instrument /Model

QuIC Financial Engineer

Simulation model

Rodrigo Rivas-Cortes

Vanilla Equity Derivatives

Allan Cowan

Inflation Swap

Curtis Sam

(Youngsuk Lee)

TRS and Repo

Jeff Hawkins

(Youngsuk Lee)

CMS and CMT

Jeremy Watson

(Paul Jones)

Non-callable Equity (Index) Swap

Allan Cowan

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4

INSTRUMENT SPECIFICATIONS

4.1

4.1.1

Cross Instrument Inputs

Map Inputs: MultiLeg

A MultiLeg aggregates a number of legs, for example a CMS payment and a Cap

on the payment.

Table 5: MultiLeg Map Definiton

Map key

Type

code

Description

Default

Constraints

strType

S

Object type

None

MultiLeg

ampLegs

AL

List of the legs to be

aggregated

Blank

Legs must exist as

maps

4.2

American Exercise Vanilla Equity Option

Table 6: Instrument 1: Model and Solver

Instrument

EQOptionAmerican

Type

Equity

Model

Black Scholes

Solution Method

Finite Difference

4.2.1

Description

The American exercise vanilla equity option will be priced with the Black-Scholes

model using a finite-difference solver. For convenience we will work with forward

equity prices

Equation 2 – Equity Options

T

S (t ) exp (u )du

t

F (t ; T )

,

DF (t , T )

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where (t) is the equity dividend yield at time t and DF(t, T) is the time t discount

factor corresponding to the deal maturity date T.3 Relative to the time T forward

measure, we have the dynamics

Equation 3 – Equity Options

dF (t ; T )

(t )dW (t )

F (t; T )

where W is a standard Brownian motion, and (t) is the volatility of the equity

S (t ) .

In this case the valuation PDE for an equity option takes the form

Equation 4 – Equity Options

1

Vt 2 (t ) F 2VFF 0,

2

where V(t, F) denotes the option price divided by the discount factor DF(t, T). The

terminal condition at maturity of the option is given by

Equation 5 – Equity Options

V (T , F (T ; T )) max ( S (T ) K ),0

V (T , F (T ; T )) max ( K S (T )),0

for the call and put option respectively. Note that

strike price

F (T ; T ) = S (T ) . The constant

K is a user defined input.

To allow for pricing to be done with a unique volatility for each scenario of each

time step in the PFE simulation, the volatility will be considered an independent

parameter in the PDE solution. From the simulated scenarios the maximum and

minimum volatility required for all risk-factor scenarios and exposure dates will be

determined, and from this we create an auxiliary axis that represents the

volatility value. The effect is that we will solve the PDE for a range of volatilities in

parallel, producing a state space indexed by time, forward stock price and

volatility: V (t , F , ) .

The state space is generated as follows. Starting from the known payoff at the

expiration date (terminal condition), we step the PDE solver back to the valuation

date. For American calls, exercise need only take place on dividend dates, while

3

Working with forward prices means that interest-rate and dividend-yield parameters make no explicit

appearance in the valuation PDE. This allows us to “cheat” in the sense that we can account for the

stochastic nature of interest rates by embedding them in the forward price instead of introducing

yet another state variable to the pricing state space. The dividend yield can be determined as

described in the HSBC document entitled "Fast CRISP Equity Options Pricing Version 1.1”, 28

February 2007.

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American puts must account for the possibility of early exercise at each

intermediate step. For simplicity in implementation, calls will be treated in the

same way as puts with exercise being account for on each intermediate time step

of the PDE solution.

At the exercise dates (dividend dates, or each time step), the continuation value

is compared to the exercise value and used as the terminal value at the next

backwards step.

Repeating this backwards recursion to the valuation date produces both the

option price as of the valuation date and a state space of option prices as a

function of forward equity price and volatility between times t and T.

The American style early exercise condition implemented at each time step of the

FD solution takes the form

Equation 6 – Equity Options

( S (t ) K )

V (t , F (t ; T ), ) max

,V (t , F (t ; T ), )

DF (t , T )

( K S (t ))

V (t , F (t ; T ), ) max

, V (t , F (t ; T ), )

DF (t , T )

for the call and put respectively.

The presence of the discount-factor term in this boundary condition forces a

modelling approximation. In general we would have to reconfigure and re-solve

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the free boundary problem every time a new PFE simulation is generated, as

DF (t , T ) is unique for each scenario. This is not practical. Instead, we

approximate by replacing the discount factor by the forward value as of the PFE

simulation start date.

Once the state space has been generated, all PFE exposure dates are looped over

to determine the value of the option for each scenario on each date. On the PFE

exposure date t scenario i is found to have the simulated equity price S i (t ) . For

this scenario we calculate the moneyness as

K / S i (t ) and time-to-maturity as

T t and interpolate into the user provided volatility matrix to find the volatility,

i , for this particular PFE date and scenario. We then calculate the forward price

Fi (t; T ) from the simulated price S i (t ) , with dividends accounted for as described

below. The value of the option on this PFE date and for this scenario, Value (t , i) , is

determined by interpolating into the state space at

multiplying by the discount factor between

i

and Fi (t ; T ) , and

t and T :

Equation 7 – Equity Options

Value (t , i) bNV (t , Fi , i ) DF (t , T )

where N is the number of shares and b is +1 if the option was bought and -1 if

sold. If this particular path was determined to be exercised at an earlier date the

price is instead set to zero. Early exercise of a scenario is determined by checking

whether the exercise value is greater than or equal to the continuation value

Equation 8 – Equity Options

wSi (t ) K V (t , Fi , i )

This exercise condition is checked every business day for puts in order to ensure

the PFE profile accurately captures the actual date the exercise occurs. If less

frequent monitoring is desired then that can be set with the parameter

strSamplingFreq in the oSolverPrefs_ input. We allow for both discrete and

continuous dividend schedules (as we will see in 4.2.1.3 Dividends). For call

options, in the regime of continuous dividends the exercise condition will be

checked daily as is done for the puts. However, in the regime of discrete

dividends the exercise condition will be checked only on the dividend payment

dates because theoretically those are the only dates that the exercise will occur.

It should be noted that daily checking in this regime could result in some

scenarios being incorrectly exercised due the under estimation of the option value

resulting from the approximation to the discount factor used in Equation 6 –

Equity Options.

The aforesaid discussion and equations in this section have assumed that the

option settles on the same day that the exercise decision is made. We will not

restrict ourselves to this settlement procedure and allow for a user specified lag

between the exercise date and settlement date. The type of settlement can have

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an impact on the exposure when a lag exists. We allow for cash settled and

physically settled options.

4.2.1.1

Cash Settled Options

A cash-settled option has the value of the option paid (received) at some date

after the exercise date. The settlement date corresponding to the final exercise

date will be provided, from this QuIC will calculate the settlement lag and this will

be used to determine the settlement date t s for each early exercise date t . The

provided holiday list and business day convention will be used to calculate the lag

and the variable settlement dates. If no final settlement date is given then there

is an nSettlementLag input that can be used to directly specify the settlement lag.

The settlement lag for cash settled options is captured in the payoff by modifying

the state space reset condition that is executed on each exercise date. Equation 6

– Equity Options becomes

Equation 9 – Equity Options

( S (t ) K ) DF (t , t s )

V (t , F (t ; T ), ) max

,V (t , F (t ; T ), )

DF (t , T )

( K S (t )) DF (t , t s )

V (t , F (t ; T ), ) max

,V (t , F (t ; T ), )

DF (t , T )

where

DF (t , t s ) is the discount factor between t and t s which accounts for the

delay in payment. As with the discount factor term in the denominator we

approximate DF (t , t s ) as the forward value as calculated from the yield curve on

the simulation start date. Note that the terminal condition (Equation 5 – Equity

Options) is modified in an analogous fashion. The effect of the lag is captured in

the state space, so the value of the trade on exposure date t for scenario i is still

given by Value (t , i) bNV (t , Fi , i ) DF (t , T ) .

However, if an option gets exercised it still has a non-zero trade value up to the

settlement date Ts . If the option expires then the trade value is zero. The value of

an exercised scenario for exposure dates between the exercise date and the

settlement date, T t Ts , is given by

Equation 10 – Equity Options

Value (t , i) bNwSi (T ) K DF (t , Ts )

where

Si (T ) is the simulated equity price on the option exercise date, Ts is the

settlement date associated with exercise date T , and w is +1 for a call option

and -1 for a put option.

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Since the exercise reset condition (Equation 9 – Equity Options) contains the

discount factor for settlement the early exercise condition must be changed

accordingly when a settlement lag exists. With a settlement lag equation

(Equation 8 – Equity Options) becomes

wSi (t ) K V (t , Fi , i ) / DF (t , Ts )

4.2.1.2

Physically Settled Options

For consistency with the front office, physically settled options are priced exactly

the same as cash-settled options except that during the settlement lag the

reported value contributing to the exposure is still subject to fluctuations in the

stock price. Hence, for exposure dates falling part way between exercise and

settlement, T t Ts , the value is a function of the simulated equity price on the

exposure date S i (t ) , rather than the price on the exercise date Si (T ) . Thus for

physically settled options equation (Equation 10 – Equity Options) becomes

Equation 11 – Equity Options

Value (t , i) bNwSi (t ) K DF (t , Ts )

For exposure dates less than the exercise date t T the state space reset

condition is again given by Equation 9 – Equity Options due to the fact that we

treat the pricing of physically and cash-settled options the same in this time

regime.

4.2.1.3

Dividends

We now consider how dividends are handled within this formulation and give

details of how the forward equity prices are calculated.

The dividend payments can be provided in two formats, either as a schedule of

discrete payments or as a continuous dividend yield. A switching date, Td , will be

provided – for dates earlier than this date we will use the discrete dividend

schedule, while for dates after the switching date we will use the dividend yield

curve to calculate a forward dividend rate.

Due to the choice of working with forward equity prices the dividends do not

enter into the solution of the PDE. However, dividends are accounted for when

calculating the forward equity price from the simulated equity prices.

On an ex-dividend date we have a jump condition for the forward price,

Equation 12 – Equity Options

F t; t j F t; t j Q j F t; t j ,

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where

F t; t j is the forward price prior to going ex-dividend on t j , F t; t j is the

forward price after going ex-dividend and

a fraction of the forward price F

Q j is the dividend amount specified as

t; t . Alternatively, we can write

j

Equation 13 – Equity Options

F t; t j 1 Q j F t; t j .

For dates t

Td T , equation (Equation 2 – Equity Options) becomes

Equation 14 – Equity Options

DF T , T

F t ;T S (t ) 1 Q j q d

,

t t T

DF t , T

j d

where each discrete dividend with ex-dividend date

t t j Td results in a factor

1 Q and the continuous dividend yield is captured through a forward discount

j

factor, DFq Td , T , calculated from the dividend yield curve.

T Td only discrete dividends apply and the forward price is obtained by

setting Td T in equation (Equation 14 – Equity Options), or

If

Equation 15 – Equity Options

1

F t; T S (t ) 1 Q j

.

t t T

DF t , T

j

Note:

If

T falls on an ex-dividend date T t j then the factor 1 Q j is

included since we are interested in the forward price after going

ex-dividend.

t Td only continuous dividends apply and the forward price is obtained by

setting Td t in equation (Equation 14 – Equity Options), or

If

Equation 16 – Equity Options

F t; T S (t )

DFq t , T

DF t , T

.

If the discrete dividend schedule is provided in terms of absolute dividend

amounts D j these will be converted to relative dividends Q j at the start of

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simulation. Specifically, if the simulation start date is

T0 then the dividends

Q j are determined iteratively through

Equation 17 – Equity Options

Qj

Dj

F T0 ; t j

,

1

F T0 ; t j S (T0 ) 1 Q k

,

T t t

DF T0 , t j

0 k j

where the

Qk have been determined already.

To apply the exercise condition for American options we need to invert (Equation

14 – Equity Options) to obtain the spot price in terms of the forward price,

Equation 18 – Equity Options

S (t ) F t; T 1 Q j

t t T

j d

This is used to calculate the

1

DF t , T

.

DFq Td , T

S (t ) needed in Equation 6 – Equity Options.

The instrument will allow for the grid to be concentrated around the strike price.

User inputs in the oSolverPrefs_ field will be available to specify the degree of

concentration as well as the location of strike price with respect to the grid points.

4.2.2

Performance Options

The American exercise instrument will also allow for the valuation of performance

options. Performance options have the payoff

S (t )

Nom * max w

Kˆ ,0

S Fix

where

S (t ) is the equity price on the exercise date and S Fix is the equity price on

a specified fixing date TFix , and Nom in the nominal amount in the currency of the

equity. Kˆ is the strike expressed as a decimal amount. Once S

is fixed the

Fix

valuation of this option follows exactly as described above but with

K Kˆ * S Fix

and the number of shares is scaled by Nom / S Fix . The value of the option is

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Value (t , i) bN

Nom

V (t , Fi , i ) DF (t , T )

S Fix

The early exercise condition, cash and physical settlement value are the same as

given in equation (Equation 8 – Equity Options), (Equation 9 – Equity Options)

K Kˆ * S Fix and

N N * Nom / S Fix . If the simulation start date T0 is after TFix then S Fix will be

and (Equation 10 – Equity Options) respectively, but with

provided as an input to the trade. If the simulation start date is before the fixing

date TFix then S Fix will be approximated as the forward price as of the simulation

start date,

S Fix F (T0 ; TFix ) . This approximated value for S Fix will be used

throughout the calculation, both for the PDE solution and pricing on each PFE date

(same value for all scenarios).

To value a performance option the input bPerformanceOption_ must be set to

TRUE. When bPerformanceOption_ is TRUE a nominal amount must be given,

rStrike must be given as a decimal amount, and dtContractStart_ will be used as

the fixing date. If the simulation starts after dtContractStart_ a historical curve

must be given or the strike and nominal must be appropriately scaled by the fixed

equity price.

4.2.3

Finite Difference Solution Preferences

The instrument will allow for various preferences to be set for the FD solution.

The number of grid points of the equity forward price and volatility axes can be

set. A Crank-Nicholson or Krylov solver can be chosen as well as a maximum time

step for the PDE solver. The grid can be concentrated around the strike price and

the volatility corresponding to the time to maturity and moneyness prevailing on

the simulation start date. Parameters indicating the degree of concentration can

be set by the user. The user can also set a frequency at which exercise is checked

during the PFE loop.

4.2.4

Transaction File Inputs

This section defines the inputs for the American exercise equity option

instrument, which is named EQOptionAmerican. All inputs must be provided and

must conform to any specification listed in the constraints column.

Table 7: Instrument 1: Transaction File Inputs

Field

No.

Input Field (Internal

Name)

Description

Type

1

strId_

Transaction ID.

String

2

strInstrument_

Instrument name.

String

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Constraints

EQOptionAmerican

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Field

No.

Input Field (Internal

Name)

Description

Type

3

strCounterparty_

String identifying

the counterparty

to which the

transaction

belongs.

String

4

strNettingGroupID_

String identifying

any netting group

to which the

transaction

belongs.

String

5

dtContractStart_

Option contract

start date.

Date

6

dtContractEnd_

Option expiry date.

Date

> dtContractStart_

7

strSettlementType_

Type of settlement

for the option.

String

CASH or PHYSICAL

8

dtSettlement_

Date on which

option is settled.

QuIC will calculate

a lag from this

date and

dtContractEnd_,

and use this lag to

calculate

dtSettlement_ for

early exercise

date.

Date

9

nSettlementLag_

Number of days

after exercise that

settlement occurs.

If cash settled, this

is date payoff is

paid, if physically

settled this is date

equity is held to.

Only used if

dtSettlement_ is

void.

Integer

≥ 0.0

10

strBoughtOrSold_

Position type.

Enum

BOUGHT, SOLD

11

strOptionType_

Option type.

Enum

CALL, PUT

12

rShares_

Number of shares.

Float

≥ 0.0

13

rStrike_

Option strike price

(in units of the

equity currency).

Float

≥ 0.0 (in units of the

equity currency)

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Constraints

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Field

No.

Input Field (Internal

Name)

Description

Type

Constraints

14

pYieldInfo_

Reference to a

yield curve

structure for the

equity currency.

String

Curve name must

exist in the market

data HDF5 file

15

pEquityInfo_

Reference to an

equity curve

structure.

String

Curve name must

exist in the market

data HDF5 file

16

pImpliedVol_

Reference to an

equity implied

volatility matrix,

matrix indexed by

time-to-maturity

and option

moneyness.

String

Curve name must

exist in the market

data HDF5 file

17

pDiscreteDividend_

Reference to a

discrete dividend

schedule

containing

dividend dates and

amounts paid per

share.

String

Curve name must

exist in the market

data HDF5 file

18

pDividendYield_

Reference to a

forward dividend

yield curve.

String

Curve name must

exist in the market

data HDF5 file

19

dtSwitchDividendType_

Date on which we

stop using

pDiscreteDividend_

and start using

pDividendYield_.

Date

20

strBusDayConv_

Business date

convention, used

to calculate

settlement date.

Enum

AFTER, BEFORE,

MODFOLLOWING

21

pg1dtHolidays_

Reference to a

holiday schedule,

used to calculate

settlement date.

String

Schedule name must

exist in the holidays

HDF5 file

22

bPerformanceOption_

Indicates if this

trade is a

performance

option.

Boolean

TRUE, FALSE

23

rNominal_

Nominal amount

used for

performance

option.

Real

This can be left blank

if

bPerformanceOption_

is FALSE

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Field

No.

Input Field (Internal

Name)

Description

Type

Constraints

24

pHistoricalEquity_

Reference to a

historical equity

curve in the

market date file,

this curve provides

the equity price on

the fixing date

(dtContractStart_).

String

Curve name must

exist in market data

HDF5 file. This input

can be left blank if

not needed. If this is

left blank when

bPerformanceOption_

is true then it is

assumed that both

rNominal and

rStrike_ have been

properly scaled by

the fixed equity

price.

25

pFXInfo_

Reference to a FX

curve used to

convert equity

currency (currency

of payoff) into the

reporting currency.

String

Curve name must

exist in the market

data HDF5 file.

26

oSolverPrefs_

Reference to a

solver preference

structure.

String

Solver ID specified in

valuation module

A sample transaction line is shown next:

Trade649,EQOptionAmerican,CPY1,GRP1,2007/05/05,2008/05/05,CASH,2008/0

5/10,5,SOLD,CALL,100,10,USD.Yield.USD,Nikkei.EquityIndex.USD,Nikkei.E

quityVolMtx.USD,Nikkei.DiscreteRelativeDividend.USD,Nikkei.Continuous

DividendYield.USD,2008/01/01,MODFOLLOWING,USD,FALSE,,,EUR.Exchange.EU

R,mpSolverPrefs

4.2.5

Auxiliary Transaction Data File Inputs

Table 8: EQOptionAmericanExerice Instrument: oSolverPrefs_ information Map

Map Key

Type

Code

Description

Constraints

anFactorGridPoints

AN

Array of number of grid

points for the forward

equity price, and

volatility.

Array of two

elements, first is the

number of grid points

for forward equity

price – second is for

volatility. Defaults is

100,50

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Map Key

Type

Code

Description

Constraints

strSamplingFreq

S

Frequency of sampling

during PFE loop to

determine if American

exercise takes place.

Default is DAILY. IF NONE

is chosen, then sampling

is on PE/EPE dates only.

NONE, DAILY,

WEEKLY, MONTHLY,

QUARTERLY,

SEMIANNUAL,

ANNUAL

rMaxTimeStep

R

Maximum time step of FD

solver.

>0.0

Defaults to 5[dy] if

blank

strSolver

S

String indicating the FD

solver type.

_xfnModExpKyrlov or

_xfnModExpCN

Defaults to

_xfnModExpKrylov if

blank

nStdDevs

N

Number of standard

deviations to use when

calculating axis

boundaries.

Defaults to 3 if blank

bUseGridConc

B

Boolean to indicate if grid

concentration should be

used.

TRUE, FALSE, Default

is TRUE

rStrikeAlpha

R

Grid concentration

parameter for

concentration around

strike price.

Default is 0.13

rVolAlpha

R

Grid concentration

parameter for

concentration around vol

as of simulation start

date.

Default is 0.4

bPlotStateSpace

B

Boolean to indicate if

state space should be

plotted, can be useful for

testing but should be

FALSE for production

runs.

TRUE, FALSE, Default

is FALSE

4.2.5.1.1

Example

An example of this solver preference map is shown next. This map will be located

in the Schedules.txt file.

mpSolverMap,{

anFactorGridPoints,AN,100

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nVolGridPoints,N,50

strSamplingFrequency,S,WEEKLY

rMaxTimeStep,R,5

strSolver,S,_xfnModExpKrylov

nStdDev,N,3

aaPts,AR,void

aaAlpha,AR,0.1

aaOnGrid,AR,FALSE

}

4.2.6

Market Data Curves

This section introduces QuIC market data curves in general, and then describes

the following types of market data curves needed to price this instrument:

Yield curve

Equity index

Equity implied volatility matrix

Discrete dividend schedule

Dividend yield curve

A complete example is provided for each of these curve types.

4.2.6.1

General Information

Transaction inputs refer to curves in a QuIC market data file with names that are

a combination of three fields in the curve data structure, in the following format:

curve-ID.curve-type.currency-ID

For example, the sample transaction in Section 4.2.2 Performance Options

specifies the equity index curve as Nikkei.EquityIndex.USD. This means that the

curve identifier is Nikkei, the curve type is EquityIndex, and the currency

identifier is USD. The curve ID is an arbitrary user-specified name, the curve type

is a predefined name determined by the QuIC curve definitions, and the currency

identifier is the standard 3-character code.

Each curve data structure includes at least these fields plus the observation date

and the data values. In addition, most curve types include certain variable

attributes and the ordinate values of the axis or axes.

Initially, you enter market data curves in text files in comma-separated value

(CSV) format. Then you use a QuIC Script program (provided with the QuIC

Analytics package) to convert these files to a single HDF5 database file.

4.2.6.2

Yield

The pYieldInfo_ transaction input (USD.Yield.USD in the sample transaction)

refers to a curve of type Yield in a market data HDF5 file.

The general format for a Yield curve in a CSV file is as follows:

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Yield, curve-ID, observation-date, currency-ID, interpolationtype, extrapolation-type, day-count-convention, compoundingfrequency, maturity-1, ..., maturity-n, yield-1, ..., yield-n

The sample yield curve includes the following variable attributes (and lets the rest

take on their default values):

Day count convention: ACT360

Compounding frequency: annual.

Table 9: Sample Yield Data shows the sample data that the curve includes.

Table 9: Sample Yield Data

Days to Maturity

Yield

30

0.0309

60

0.0315902

91

0.032243

182

0.0340263

273

0.0354036

365

0.036532

730

0.039369

1096

0.04095

1460

0.0421268

1825

0.0431881

2555

0.0451795

3650

0.0480538

5475

0.0488034

7300

0.0503278

10950

0.0510875

Figure 1: Sample Yield Curve (CSV Format) shows how the sample curve is coded

in a CSV file. In the file, the curve occupies a single line, but in this figure it

wraps to show the whole line.

Figure 1: Sample Yield Curve (CSV Format)

Yield,USD,2005/05/05,USD,,,ACT360,ANNUAL,30,60,91,182,273,365,730,1096,1460,

1825,2555,3650,5475,7300,10950,0.0309,0.0315902,0.032243,0.0340263,

0.0354036,0.036532,0.039369,0.04095,0.0421268,0.0431881,0.0451795,0.0480538,

0.0488034,0.0503278,0.0510875

4.2.6.3

Equity Index

The pEquityInfo_ transaction input (Nikkei.EquityIndex.USD in the sample

transaction) refers to a curve of type EquityIndex in a market data HDF5 file.

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The general format for an EquityIndex curve in a CSV file is as follows:

EquityIndex, curve-ID, observation-date, currency-ID, index-value

Figure 2: Sample EquityIndex Curve (CSV Format) shows an example of the

equity curve as it appears in a CSV file.

Figure 2: Sample EquityIndex Curve (CSV Format)

EquityIndex,Nikkei,2005/03/09,USD,11073.77

4.2.6.4

Equity Implied Volatility

The pImpliedVol_ transaction input (Nikkei.EquityImpliedVolMtx.USD in the

sample transaction) refers to a curve of type EquityImpliedVolMtx in a market

data HDF5 file.

The general format for an EquityImpliedVolMtx curve in a CSV file is as follows:

EquityImpliedVolMtx, curve-ID, observation-date, currency-ID,

moneyness-interpolation-type, moneyness-extrapolation-type,

expiry-interpolation-type, expiry-extrapolation-type, day-countconvention, days-per-annum, moneyness-1, volatility-1,...,

volatility-n

...

EquityImpliedVolMtx, curve-ID, observation-date, currency-ID,

moneyness-interpolation-type, moneyness-extrapolation-type,

expiry-interpolation-type, expiry-extrapolation-type, day-countconvention, days-per-annum, moneyness-m, volatility-1,...,

volatility-n

The curve is specified by multiple lines, one for each row of the matrix. The

moneyness axis in this matrix is defined as K/S(t=0), where S(t=0) is the spot

equity price on the simulation start date, and K is the strike price.

The sample volatility matrix curve specifies the following variable attributes:

Moneyness interpolation method: linear

Moneyness extrapolation method: nearest

Expiry interpolation method: linear

Expiry extrapolation method: nearest

Day count convention: ACT360

Days per annum: 360.

Table 10: Sample Equity Implied Volatility Data shows the sample data that the

curve includes (for simplicity, only a subset of a typical matrix is included in this

example).

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Table 10: Sample Equity Implied Volatility Data

Maturity (months)

Moneyness

1

2

3

6

9

12

18

0.9

0.219123

0.202728

0.19436

0.183323

0.179931

0.176813

0.176943

0.95

0.181194

0.172552

0.168963

0.164444

0.1643

0.163275

0.166247

0.975

0.162097

0.157358

0.156172

0.15494

0.156427

0.156516

0.16087

1.0

0.143746

0.142771

0.143874

0.145719

0.148816

0.150071

0.155677

1.025

0.127188

0.129412

0.132495

0.137071

0.141624

0.14395

0.150716

1.05

0.112311

0.117199

0.121977

0.12896

0.134825

0.138135

0.145974

1.075

0.1

0.10606

0.112264

0.121354

0.128397

0.132607

0.141439

Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format) shows how this curve

is coded in a CSV file. In this figure, each line wraps to show the whole line.

Figure 3: Sample EquityImpliedVolMtx Curve (CSV Format)

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.9,1,

2,3,6,9,12,18,0.219123,0.202728,0.19436,0.183323,0.179931,0.176813,0.176943

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.95,1,

2,3,6,9,12,18,0.181194,0.172552,0.168963,0.164444,0.1643,0.163275,0.166247

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,0.975,

1,2,3,6,9,12,18,0.162097,0.157358,0.156172,0.15494,0.156427,0.156516,0.16087

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1,1,2,

3,6,9,12,18,0.143746,0.142771,0.143874,0.145719,0.148816,0.150071,0.155677

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.025,

1,2,3,6,9,12,18,0.127188,0.129412,0.132495,0.137071,0.141624,0.14395,

0.150716

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.05,1,

2,3,6,9,12,18,0.112311,0.117199,0.121977,0.12896,0.134825,0.138135,0.145974

EquityImpliedVolMtx,FTSE,2007/04/27,EUR,lin,near,lin,near,ACT360,360,1.075,

1,2,3,6,9,12,18,0.1,0.10606,0.112264,0.121354,0.128397,0.132607,0.141439

4.2.6.5

Discrete Dividend Schedule

The pDiscreteDividend_ transaction input

(Nikkei.DiscreteAbsoluteDividend.USD in the sample transaction) refers to a

curve of type DiscreteAbsoluteDividend in a market data HDF5 file.

The general format for a DiscreteAbsoluteDividend curve in a CSV file is:

DiscreteAbsoluteDividend, curve-ID, observation-date, currency-ID,

interpolation-type, extrapolation-type, date-1, ..., date-n,

dividend-1, ..., dividend-n

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The sample dividend schedule curve does not specify any variable attributes (it

lets them take their defaults). Table 11: Sample Dividend Schedule Data shows

the sample data the curve includes.

Table 11: Sample Dividend Schedule Data

Date

Absolute Dividend Amount

2005/05/26

20

2005/06/27

20

2005/07/26

20

2005/08/26

20

2005/09/27

20

2005/11/25

20

2005/12/27

20

2006/01/26

20

2006/02/15

20

2006/02/23

20

2006/03/28

20

2006/05/26

20

2006/06/27

20

2006/07/26

20

2006/08/28

20

2006/09/26

20

2006/11/27

20

2006/12/26

20

2007/01/26

20

2007/02/15

20

2007/02/23

20

Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format) shows how this

curve is coded in a CSV file. In the file, the curve occupies a single line, but in

this figure it wraps to show the whole line.

Figure 4: Sample DiscreteAbsoluteDividend Curve (CSV Format)

DiscreteAbsoluteDividend,Nikkei,2005/03/09,USD,,,2005/05/26,2005/06/27,

2005/07/26,2005/08/26,2005/09/27,2005/11/25,2005/12/27,2006/01/26,

2006/02/15,2006/02/23,2006/03/28,2006/05/26,2006/06/27,2006/07/26,

2006/08/28,2006/09/26,2006/11/27,2006/12/26,2007/01/26,2007/02/15,

2007/02/23,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,

20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0,20.0

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When the discrete dividend schedule is provided as an absolute amount (as

shown in the example), it will be converted to a relative amount with respect to

forward prices calculated on the simulation start date, as shown in Equation 16 –

Equity Options.

The discrete dividend schedule can also be provided directly as a relative amount.

The curve has the same format as above, however the name is now

DiscreteRelativeDividend. These amounts will be directly used as the relative

dividend amounts on each date.

4.2.6.6

Dividend Yield Curve

The pDividendYield_ transaction input (Nikkei.USD in the sample transaction)

refers to a curve of type DividendYield in a market data HDF5 file.

The general format for a DividendYield curve in a CSV file is as follows:

DividendYield, curve-ID, observation-date, currency-ID,

interpolation-type, extrapolation-type, day-count-convention,

compounding-frequency, date-1, ..., date-n, yield-1, ..., yield-n

The sample dividend yield curve specifies the following variable attribute (and lets

the others take on their default values):

Day count convention: ACT365

Compounding frequency: continuous

Table 12: Sample Dividend Yield Data shows the sample data that the curve

includes.

Table 12: Sample Dividend Yield Data

Date

Dividend Yield

2005/06/05

0.02

2005/07/05

0.021

2005/08/05

0.022243

2005/11/05

0.0240263

2006/02/05

0.0254036

2006/05/05

0.026532

2007/05/05

0.029369

2008/05/05

0.03095

2009/05/05

0.0321268

2010/05/05

0.0331881

2011/05/05

0.0351795

2012/05/05

0.0380538

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Date

Dividend Yield

2013/05/05

0.0388034

2014/05/05

0.0403278

2015/05/05

0.0410875

Figure 5: Sample DividendYield Curve (CSV Format) shows how this curve is

coded in a CSV file. In the file, the curve occupies a single line, but in this figure

it wraps to show the whole line.

Figure 5: Sample DividendYield Curve (CSV Format)

DividendYield,Nikkei,2005/05/05,USD,,,ACT365,CONTINUOUS,2005/06/05,2005/07/0

5,2005/08/05,2005/11/05,2006/02/05,2006/05/05,2007/05/05,2008/05/05,2009/05/

05,2010/05/05,2011/05/05,2012/05/05,2013/05/05,2014/05/05,2015/05/05,0.02,0.

021,0.022243,0.0240263,0.0254036,0.026532,0.029369,0.03095,0.0321268,0.03318

81,0.0351795,0.0380538,0.0388034,0.0403278,0.0410875

4.2.7

Definition of Daycounts

The following table defines the daycounts that can be used with the above curves.

Table 13: Day count Convention Codes

Value

Meaning

ACTACT

Uses the actual number of days in the month

and year.

ACT365

Same as ACTACT.

ACT365FIXED

Uses the actual number of days in the month

and year, but days in a leap year count as

1/365th of a year.

ACT360

Interest is calculated over the actual number of

calendar days, on the basis of a 360-day year.

THIRTY360

Assumes there are 30 days in a month and 360

days in a year.

EURO30360

Essentially the same as 30360 but used for

Eurobonds and many foreign bonds.

The one distinction is that whenever the start or

end date is the 31st of the month, it is reset to

the 30th. The 30360 version only resets the end

date when the start date is on the 30th or 31st.

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4.2.8

Testing Methodology

See CRISP New Products Testing Strategy V0.3 (located in the HSBC Credit Risk

New Products Programme Lotus works space) and QFT Instrument Testing.

4.3

European Exercise Vanilla Equity Option

Table 14: Instrument 2: Model and Solver

Instrument

EQOptionEuropeanExercise

Type

Equity

Model

Black-Scholes

Solution Method

Analytic

4.3.1

Description

The European exercise vanilla equity option will be valued using the analytic

Black-Scholes formula. Once again we will work with forward equity price

Equation 19 – Equity Options

T

S (t ) exp (u )du

t

F (t ; T )

,

DF (t , T )

where (t) is the equity dividend yield at time t and DF(t, T) is the time t discount

factor corresponding to the deal maturity date T. The option price divided by the

discount factor DF(t, T) is given by the solution to the PDE

Equation 20 – Equity Options

1

Vt 2 (t ) F 2VFF 0,

2

which is given by

Equation 21 – Equity Options

V (t , F , ) bNw[ F (t; T )(wd1 ) K(wd 2 )],

Where

Equation 22 – Equity Options

F (t; T ) 1 2

ln

v (t , T )

T

K 2

d1

, d 2 d1 v(t , T ), v 2 (t , T ) 2 ( x)dx

t

v(t , T )

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