Hull J.C. Risk management and Financial institutions
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CONTENTS IN BRIEF
Business Snapshots xiii
Preface xv
1. Introduction 1
2. Financial Products and How They are Used for Hedging 27
3. How Traders Manage Their Exposures 55
4. Interest Rate Risk 79
5. Volatility 1ll
6. Correlation and Copulas 143
7. Bank Regulation and Basel II 165
8. The VaR Measure 195
9. Market Risk VaR: Historical Simulation Approach 217
10. Market Risk VaR: Model-Building Approach 233
11. Credit Risk: Estimating Default Probabilities 255
12. Credit Risk Losses and Credit VaR 277
13. Credit Derivatives 299
14. Operational Risk 321
15. Model Risk and Liquidity Risk 343
16. Economic Capital and RAROC 365
17. Weather, Energy, and Insurance Derivatives 385
18. Big Losses and What We Can Learn from Them 395
Appendix A: Valuing Forward and Futures Contracts 407
Appendix B: Valuing Swaps 409
Appendix C: Valuing European Options 413
Appendix D: Valuing American Options 417
Appendix E: Manipulation of Credit Transition Matrices 421
Answers to Questions and Problems 423
Glossary of Terms 457
Derivagem Software 479
Tables for N(x) 484
Index 487
Contents
Business Snapshots xiii
Preface xv
Chapter 1 Introduction 1
1.1 Risk vs. return for investors 2
1.2 Risk vs. return for companies 12
1.3 Bank capital 15
1.4 Approaches to managing risk 18
1.5 The management of net interest income 20
Summary 22
Further reading 23
Questions and problems 24
Assignment questions 25
Chapter 2 Financial products and how they are used for hedging 27
2.1 The markets 27
2.2 When to hedge 28
2.3 The "plain vanilla" products 30
2.4 Using the products for hedging 43
2.5 Exotic options and structured deals 46
2.6 Dangers 48
Summary 48
Further reading 50
Questions and problems 50
Assignment questions 53
Chapter 3 How traders manage their exposures 55
3.1 Delta 55
3.2 Gamma 63
3.3 Vega 65
3.4 Theta 67
3.5 Rho 69
3.6 Calculating Greek letters 69
3.7 Taylor series expansions 70
3.8 The realities of hedging 72
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Contents
3.9 Hedging exotics 73
3.10 Scenario analysis 74
Summary 75
Further reading 76
Questions and problems 76
Assignment questions 78
Chapter 4 Interest rate risk 79
4.1 Measuring interest rates 80
4.2 Zero rates and forward rates 83
4.3 Treasury rates 85
4.4 LIBOR and swap rates 87
4.5 Duration 89
4.6 Convexity 93
4.7 Application to portfolios 94
4.8 Nonparallel yield curve shifts 96
4.9 Interest rate deltas 98
4.10 Principal components analysis 100
4.11 Gamma and vega 104
Summary 105
Further reading 106
Questions and problems 106
Assignment questions 108
Chapter 5 Volatility 111
5.1 Definition of volatility 112
5.2 Implied volatilities 114
5.3 Estimating volatility from historical data 115
5.4 Are daily percentage changes in financial variables
normal? 117
5.5 Monitoring daily volatility 121
5.6 The exponentially weighted moving average model 123
5.7 The GARCH(1,1) model 125
5.8 Choosing between the models 127
5.9 Maximum-likelihood methods 127
5.10 Using GARCH(1,1) to forecast future volatility 133
Summary 137
Further reading 138
Questions and problems 139
Assignment questions 140
Chapter 6 Correlations and Copulas 143
6.1 Definition of correlation 144
6.2 Monitoring correlation 146
6.3 Multivariate normal distributions 149
Contents ix
6.4 Copulas 152
6.5 Application to loan portfolios 159
Summary 161
Further reading 161
Questions and problems 162
Assignment questions 163
Chapter 7 Bank regulation and Basel II 165
7.1 Reasons for regulating bank capital 167
7.2 Pre-1988 168
7.3 The 1988 BIS Accord 169
7.4 The G-30 policy recommendations 172
7.5 Netting 174
7.6 The 1996 Amendment 176
7.7 Basel II 178
7.8 Credit risk capital under Basel II 179
' 7.9 Operational risk under Basel II 188
7.10 Supervisory review 189
7.11 Market discipline 190
Summary 191
Further reading 192
Questions and problems 192
Assignment questions 194
Chapter 8 The VaR measure 195
8.1 Definition of VaR 196
8.2 VaR vs. expected shortfall 198
8.3 Properties of risk measures 199
8.4 Choice of parameters for VaR 202
8.5 Marginal VaR, incremental VaR, and component VaR... 206
8.6 Back testing 208
8.7 Stress testing 212
Summary 213
Further reading 214
Questions and problems 215
Assignment questions 216
Chapter 9 Market risk VaR: historical simulation approach 217
9.1 The methodology 217
9.2 Accuracy 220
9.3 Extensions 221
9.4 Extreme value theory 224
9.5 Application 227
Summary 229
Further reading 230
x Contents
Questions and problems 231
Assignment questions 231
Chapter 10 Market risk VaR: model-building approach 233
10.1 The basic methodology 234
10.2 The linear model 237
10.3 Handling interest rates 238
10.4 Applications of the linear model 242
10.5 The linear model and options 242
10.6 The quadratic model 246
10.7 Monte Carlo simulation 248
10.8 Using distributions that are not normal 249
10.9 Model building vs. historical simulation 250
Summary 251
Further reading 252
Questions and problems 252
Assignment questions 254
Chapter 11 Credit risk: estimating default probabilities 255
11.1 Credit ratings 255
11.2 Historical default probabilities 258
11.3 Recovery rates 260
11.4 Estimating default probabilities from bond prices 261
11.5 Comparison of default probability estimates 265
11.6 Using equity prices to estimate default probabilities 269
Summary 272
Further reading 273
Questions and problems 273
Assignment questions 275
Chapter 12 Credit risk losses and credit VaR 277
12.1 Estimating credit losses 278
12.2 Credit risk mitigation 283
12.3 Credit VaR 287
12.4 Vasicek's model 287
12.5 Credit Risk Plus 288
12.6 CreditMetrics 289
12.7 Interpreting credit correlations 293
Summary 295
Further reading 295
Questions and problems 296
Assignment questions 297
Chapter 13 Credit derivatives 299
13.1 Credit default swaps 299
13.2 Credit indices 303
Contents
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13.3 Valuation of credit default swaps 303
13.4 CDS forwards and options 308
13.5 Total return swaps 310
13.6 Basket credit default swaps 311
13.7 Collateralized debt obligations 311
13.8 Valuation of a basket CDS and CDO 314
Summary 316
Further reading 317
Questions and problems 317
Assignment questions 319
Chapter 14 Operational risk 321
14.1 What is operational risk? 323
14.2 Determination of regulatory capital 324
14.3 Categorization of operational risks 326
14.4 Loss severity and loss frequency 327
14.5 Forward looking approaches 331
14.6 Allocation of operational risk capital 333
14.7 Use of the power law 335
14.8 Insurance 335
14.9 Sarbanes-Oxley 337
Summary 338
Further reading 339
Questions and problems 340
Assignment questions 340
Chapter 15 Model risk and liquidity risk 343
15.1 The nature of models in finance 344
15.2 Models for nonlinear products 345
15.3 Models for actively traded products 346
15.4 Models for structured products 351
15.5 Dangers in model building 352
15.6 Detecting model problems 353
15.7 Traditional view of liquidity risk 354
15.8 Liquidity black holes 356
15.9 Long-term capital management 360
15.10 Liquidity vs. profitability 361
Summary 362
Further reading 363
Questions and problems 363
Assignment questions 364
Chapter 16 Economic capital and RAROC 365
16.1 Definition of economic capital 366
16.2 Components of economic capital 368
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16.3 Shapes of the loss distributions 370
16.4 Relative importance of risks 372
16.5 Aggregating economic capital 373
16.6 Allocation of the diversification benefit 377
16.7 Deutsche Bank's economic capital 378
16.8 RAROC 379
Summary 381
Further reading 381
Questions and problems 381
Assignment questions 382
Chapter 17 Weather, energy, and insurance derivatives 385
17.1 Weather derivatives 385
17.2 Energy derivatives 387
17.3 Insurance derivatives 390
Summary 391
Further reading 392
Questions and problems 393
Assignment question 394
Chapter 18 Big losses and what we can learn from them 395
18.1 Risk limits 397
18.2 Managing the trading room 399
18.3 Liquidity risk 402
18.4 Lessons for nonfinancial corporations 404
Summary 406
Further reading 406
Appendix A: Valuing forward and futures contracts 407
Appendix B: Valuing swaps 409
Appendix C: Valuing European options 413
Appendix D: Valuing American options 417
Appendix E: The manipulation of credit transition matrices 421
Answers to questions and problems 423
Glossary of terms 457
DerivaGem software 479
Table for N(x) when x < 0 484
Table for N(x) when x > 0 485
Index 487
BUSINESS SNAPSHOTS
1.1 The Hidden Costs of Bankruptcy 14
1.2 Expensive Failures of Financial Institutions in the US 22
2.1 The Unanticipated Delivery of a Futures Contract 35
2.2 Procter and Gamble's Bizarre Deal 39
2.3 Microsoft's Hedging 47
2.4 The Barings Bank Disaster 49
3.1 Hedging by Gold Mining Companies 58
3.2 Dynamic Hedging in Practice 72
3.3 Is Delta Hedging Easier or More Difficult for Exotics 73
4.1 Orange County's Yield Curve Plays 85
5.1 What Causes Volatility? 113
5.2 Making Money from Foreign Currency Options 118
7.1 Systemic Risk 168
7.2 Basel III? 189
8.1 Historical Perspectives on VaR 196
11.1 Risk-Neutral Valuation 267
12.1 Long-Term Capital Management's Big Loss 285
12.2 Downgrade Triggers and Enron's Bankruptcy 286
13.1 Who Bears the Credit Risk? 301
13.2 Is the CDS Market a Fair Game? 309
13.3 Correlation Smiles 315
14.1 The Hammersmith and Fulham Story 332
14.2 Rogue Trader Insurance 337
15.1 Kidder Peabody's Embarrassing Mistake 345
15.2 Exploiting the Weaknesses of a Competitor's Model 346
15.3 Crashophobia 349
15.4 The Crash of 1987 358
15.5 British Insurance Companies 359
15.6 Metallgesellschaft 362
16.1 The EGT Fund 373
18.1 Big Losses 396
Preface
This book is based on an elective course entitled Financial Risk Manage-
ment I have taught at University of Toronto for many years. The main
focus of the book is on the risks faced by banks and other financial
institutions, but much of the material presented is equally important to
nonfinancial institutions. Like my popular text Options, Futures, and
Other Derivatives, this book is designed to be useful to practitioners as
well as college students.
The book is appropriate for elective courses in either risk management
or the management of financial institutions. It is not necessary for students
to take a course on options and futures markets prior to taking a course
based on this book, but if they have taken such a course much of the
material in the first four chapters will not need to be covered. Chapter 13
on credit derivatives and Chapter 17 on weather, energy, and insurance
derivatives can be skipped if this material is covered elsewhere or is not
considered appropriate. Chapter 18 on big losses and what we can learn
from them is a great chapter for the last class of a course because it draws
together many of the points made in earlier chapters.
The level of mathematical sophistication in the way material is pre-
sented has been managed carefully so that the book is accessible to as
wide an audience as possible. For example, when covering copulas in
Chapter 6, I present the intuition followed by a detailed numerical
example; when covering maximum-likelihood methods in Chapter 5
and extreme value theory in Chapter 9, I provide numerical examples
and enough details for readers to develop their own Excel spreadsheets.
This is a book about risk management and so there is very relatively little
material on the valuation of derivatives contracts. (This is the main focus
my other two books Options, Futures, and Other Derivatives and
Fundamentals of Futures and Options Markets.) For reference, I have
included at the end of the book appendices that summarize some of
the key derivatives pricing formulas that are important to risk managers.