The credit risk of complex derivatives

Erik Banks

The Credit Risk

of Complex

Derivatives

Third Edition

THE CREDIT RISK OF COMPLEX DERIVATIVES

ERIK BANKS

The Credit Risk

of Complex

Derivatives

Third Edition

© Erik Banks 2004

All rights reserved. No reproduction, copy or transmission of this publication may be

made without written permission.

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accordance with the Copyright, Designs and Patents Act 1988.

First published 2004 by

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To my wife, Milena

List of Figures x

List of Tables xiv

Preface xvi

PART I DERIVATIVES, CREDIT, AND RISK MANAGEMENT

1 An Overview of the Derivatives Marketplace 3

Derivatives Market Scope 4

Market Volatility and the Growth of Derivatives 10

General Derivative Risk and Return Considerations 15

Addressing Derivative Risk Management Issues 19

Overview of the Text 25

2 Derivative Losses 27

Sources of Derivative Losses 27

A Sampling of Derivative Losses 30

3 Risk Governance and Risk Management 42

Corporate and Risk Governance 42

Credit Risk Management Processes 43

4 Regulatory and Industry Initiatives 54

Regulatory Efforts 54

Industry Efforts 68

vii

Contents

Part II THE CREDIT RISK OF COMPLEX DERIVATIVES

5 Classification and Quantification of Credit Risk 81

Background 81

Market Risk 82

Risk Equivalency 86

Risk Factors 88

The Risk Equivalency Framework 98

Refining Risk Equivalent Exposure 101

Simulation: An Alternative Methodology 105

6 Quantifying Option Credit Risk 108

An Overview of Option Credit Risk 109

7 The Credit Risk of Compound Option Strategies 121

Product Description 122

Credit Risk Quantification 138

8 The Credit Risk of Complex Options 160

Product Description 164

Credit Risk Quantification 202

9 Quantifying Swap Credit Risk 241

Actual Exposure of Swap Contracts 242

Fractional Exposure of Swap Contracts 246

Swap Credit Risk in a Complete Framework 248

A Model for Calculating Swap Credit Risk 250

Empirical Findings on Swap Risk Factors 256

10 The Credit Risk of Complex Swaps 260

Product Description 261

Credit Risk Quantification 288

Part III CREDIT PORTFOLIO RISK MANAGEMENT ISSUES

11 Credit Risk Management of Derivative Portfolios:

Quantitative Issues 321

Consolidating Individual Credit Exposures into Portfolios 322

Portfolios of Counterparties 341

Quantifying Credit Losses 342

12 Credit Risk Portfolio Models 367

Value-at-Risk and Regulatory Models 367

viii CONTENTS

The Ideal Generic Credit Portfolio Model 369

An Overview of Specific Credit Risk Portfolio Models 376

13 Credit Risk Management of Derivative Portfolios:

Qualitative Issues 385

Managing Derivative Credit Exposures Dynamically 385

Addressing Ancillary Credit Risk Management Issues 412

Appendix 1: Option Valuation 420

Appendix 2: Twenty Questions for the Derivatives Desk 428

Appendix 3: ISDA 2002 Master Agreement 430

Notes 467

Glossary 494

Bibliography 541

Index 549

CONTENTS ix

1.1 General classification of derivatives 6

1.2 General classification of swaps 8

1.3 General classification of options 8

1.4 Derivative asset classes 9

1.5 Eurodollars (US$ Libor), 15-year average volatility (%),

1988–2002 11

1.6 30-Year US Treasury bond, 15-year average volatility,

1988–2002 12

1.7 S&P500 index, 15-year average volatility, 1988–2002 12

1.8 Crude oil (light sweet crude), 15-year average volatility,

1988–2002 12

1.9 Gold, 15-year average volatility, 1988–2002 13

1.10 US$/Japanese yen, 15-year average volatility, 1988–2002 13

1.11 US$/Pound Sterling, 15-year average volatility, 1988–2002 13

1.12 Notional outstandings, OTC derivative contracts,

1987–2002 14

1.13 Gross replacement cost, OTC derivative contracts,

1998–2002 15

1.14 Risk-adjusted returns 17

1.15 Common credit risk mitigation techniques 23

3.1 Board level credit risk management duties 44

3.2 Corporate risk management duties 45

3.3 Sources of credit risk in a financial institution 46

3.4 Credit risk governance process 53

4.1 Forms of regulatory and economic capital 57

4.2 BIS IRB approaches 65

x

List of Figures

5.1 Normal distribution 89

5.2 Lognormal distribution 89

5.3 Path of the risk factor at 10% volatility,

97.5% confidence level 98

5.4 Path of the risk factor at 10% volatility,

varying confidence levels (90–99%) 98

5.5 Path of the risk factor at 97.5% confidence level,

varying volatilities (10–30%) 99

5.6 The risk equivalency process 100

5.7 Alternative risk exposure paths 104

5.8 Sample asset price paths 107

7.1 Long call payoff profile 123

7.2 Long put payoff profile 123

7.3 Short call payoff profile 124

7.4 Short put payoff profile 124

7.5 Bullish vertical call spread payoff profile 126

7.6 Bearish vertical put spread payoff profile 127

7.7 Long straddle payoff profile 128

7.8 Short straddle payoff profile 129

7.9 Long strangle payoff profile 130

7.10 Short strangle payoff profile 130

7.11 Long butterfly payoff profile 131

7.12 Short butterfly payoff profile 132

7.13 Long condor payoff profile 133

7.14 Short condor payoff profile 133

7.15 Call backspread payoff profile 135

7.16 Call ratio vertical spread payoff profile 136

7.17 Synthetic long payoff profile 139

7.18 Synthetic short payoff profile 139

7.19 Bullish vertical call spread with a single counterparty 143

7.20 Bullish vertical call spread with multiple counterparties 144

8.1 Up and out call option 167

8.2 Down and in put option 167

8.3 Average price put option 168

8.4 Average strike put option 170

8.5 Floating strike lookback call option 171

8.6 Put option on the minimum 172

8.7 High–low option 173

8.8 Partial lookback call option 175

8.9 Ladder call option 176

8.10 Cliquet put option 177

FIGURES xi

8.11 Shout put option 179

8.12 Installment call option 180

8.13 Cash-or-nothing at hit put option 182

8.14 Option on the best of two assets and cash 183

8.15 Put option on the worst of two assets 185

8.16 Multiple strike call option 187

8.17 Spread call option 188

8.18 Basket call option 191

8.19 Compound call option 193

8.20 Regular chooser option 194

8.21 Contingent premium call option 195

8.22 Deferred payment American call option 196

8.23 Quanto option on put structure 197

8.24 Exploding call option 199

8.25 Squared power call option 200

9.1 The simulation approach to credit risk valuation 249

9.2 Swap replacement cost curve 256

10.1 Inverse floater swap 264

10.2 Pay/receive flows of leveraged swaps 265

10.3 Leveraged swap 266

10.4 Leveraged inverse floater swap 266

10.5 Differential swap 267

10.6 Creation of a US$ Libor/Euribor differential swap 268

10.7 Amortizing swap 269

10.8 Mortgage swap 271

10.9 Index principal swap 272

10.10 Reverse index principal swap 273

10.11 Credit forward 275

10.12 Default swap 276

10.13 Total return swap 279

10.14 Equity call swap 280

10.15 Equity call–put swap 281

10.16 Realized volatility swap 283

10.17 Zero coupon inflation swap 285

10.18 Peak electricity swap 286

10.19 Cooling degree day swap 288

10.20 Decomposing a leveraged inverse floater swap 292

11.1 Credit transaction decision process 325

11.2 Maximum peak and forward point exposures 336

11.3 Forward point exposures 1 337

xii FIGURES

11.4 Forward point exposures 2 338

11.5 Derivation of possible credit losses 342

11.6 REE probability distribution 345

11.7 Default rate probability distribution 350

11.8 Recovery rate probability distribution 352

11.9 Creation of a credit loss distribution function 353

11.10 Expected credit losses 354

11.11 Worst-case credit losses 357

11.12 Expected, unexpected, and worst-case credit losses 360

11.13 Generalized credit process 366

12.1 PDF of future asset value and probability of default 373

12.2 Inputs and outputs of the generic credit risk portfolio

model 375

13.1 Systematic and idiosyncratic credit risks 388

13.2 Credit forward to create credit capacity 399

13.3 Dynamic credit exposure management 413

FIGURES xiii

1.1 Countries amending legislation to accept netting 23

4.1 BIS CEM factors, 1988 (percentages) 59

4.2 BIS OEM factors, 1988 (percentages) 60

4.3 BIS CEM factors, 1994–5 (percentages 60

4.4 Best practice self-regulation 72

5.1 PMR and AMR over trade life 85

5.2 Counterparty risk, market risk, and losses 86

5.3 Probabilities and z factors 94

5.4 Confidence levels and z factors 95

5.5 Sample table of Nikkei risk factors: constant 10%

volatility, varying confidence levels 97

5.6 Sample table of Nikkei risk factors: constant 97.5%

confidence levels, varying volatilities 97

5.7 Alternative REE computations 104

6.1 Ongoing credit risk of a put option 114

7.1 Option risk sensitivities: simple position directional strategies 125

7.2 Option risk sensitivities: compound position directional

strategies 127

7.3 Option risk sensitivities: compound position volatility

strategies 136

7.4 Synthetic options 138

7.5 Synthetic underlyings 138

8.1 Complex option variations 162

8.2 Barrier options 165

xiv

List of Tables