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CONTENTS
Preface ... xix
Part 1 Why Risk Management? ... 1
Chapter 1 Introduction ... 3
1.1. The growth of derivatives markets ... 5
1.2. Some basic ideas concerning derivatives as risk...
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CONTENTS
Preface ... xix
Part 1 Why Risk Management? ... 1
Chapter 1 Introduction ... 3
1.1. The growth of derivatives markets ... 5
1.2. Some basic ideas concerning derivatives as risk management tools ... 8
1.2.1. Options ... 8
1.2.2. Forward contracts ... 10
1.3. Using derivatives the right way for risk management ... 14
1.4. What does it take to use derivatives the right way for risk management? ... 16
1.4.1. Designing a foreign exchange hedging program at Merck ... 16
1.4.2. Measuring risks at Microsoft ... 17
1.5. Learning to manage risks with derivatives the right way ... 18
Key Concepts ... 20
Literature Note ... 20
Chapter 2 Investors and Risk Management ... 21
2.1. Evaluating the risk and the return of individual securities and portfolios ... 22
2.1.1. The distribution of the return of IBM ... 23
2.1.2. The distribution of the return of a portfolio ... 27
2.2. Diversification, asset allocation, and expected returns ... 30
2.2.1. Diversification and the return of a portfolio ... 30
2.2.2. Asset allocation when there is a risk-free asset ... 32
2.2.3. The risk of a security in a diversified portfolio ... 34
2.2.4. The capital asset pricing model ... 35
2.3. Diversification and risk management ... 36
2.3.1. Risk management and shareholder wealth ... 40
2.3.2. Risk management and shareholder clienteles ... 42
2.3.3. The risk management irrelevance proposition ... 45
2.4. Summary ... 46
Key Concepts ... 46
Review Questions ... 46
Questions and Exercises ... 47
Literature Note ... 48
Chapter 3 Creating Value with Risk Management ... 51
3.1. Bankruptcy costs and costs of financial distress ... 53
3.1.1. Bankruptcy costs and firm value ... 57
3.1.2. Bankruptcy costs, financial distress costs, and the costs of risk management programs ... 58
3.1.3. Bankruptcy costs, Homestake, and Enron ... 59
3.2. Taxes and risk management ... 59
3.2.1. The tax argument for risk management ... 62
3.2.2. The tax benefits of risk management and Homestake ... 63
3.3. Optimal capital structure and risk management ... 63
3.3.1. The tax shield of debt, costs of financial distress, and risk management ... 64
3.3.2. Does Homestake have too little debt? ... 65
3.4. Should the firm hedge to reduce the risk of large undiversified shareholders? ... 66
3.4.1. Large undiversified shareholders can increase firm value ... 66
3.4.2. Risk and the incentives of managers ... 67
3.4.3. Large shareholders, managerial incentives, and Homestake ... 68
3.5. Stakeholders ... 68
3.5.1. When should firms care about stakeholders? ... 68
3.5.2. Stakeholders and Homestake ... 69
3.6. Risk management, financial distress, and investment ... 69
3.6.1. Debt overhang ... 70
3.6.2. Information asymmetries and agency costs of managerial discretion ... 71
3.6.3. The cost of external funding and Homestake ... 72
3.7. Summary ... 74
Key Concepts ... 75
Review Questions ... 75
Literature Note ... 75
Chapter 4 A Firm-Wide Approach to Risk Management ... 77
4.1. Measuring risk for corporations ... 79
4.1.1. Measuring value at risk in a financial firm ... 79
4.1.2. Implementing VaR ... 87
4.1.3. Measuring cash flow at risk in a nonfinancial firm ... 89
4.1.4. VaR or CaR? ... 91
4.2. VaR, CaR, and firm value ... 92
4.2.1. The impact of projects on VaR ... 93
4.2.2. Evaluating the impact of a large project on CaR ... 97
4.2.3. Allocating the cost of CaR or VaR to existing activities ... 99
4.3. Managing firm risk measured by VaR or CaR ... 103
4.3.1. Reducing the cost of risk for a given level of VaR or CaR ... 103
4.3.2. Reducing risk through project choice ... 106
4.3.3. Using derivatives and other financial instruments to reduce risk ... 106
4.4. Summary ... 107
Key Concepts ... 108
Review Questions ... 108
Questions and Exercises ... 108
Literature Note ... 110
Part 2 Heading with Forwards, Futures, and Options Contracts ... 111
Chapter 5 Forward and Futures Contracts ... 113
5.1. Pricing forward contracts on T-bills ... 115
5.1.1. Valuing a forward position using the method of pricing by arbitrage ... 115
5.1.2. A general pricing formula ... 120
5.1.3. Pricing the contract after inception ... 120
5.2. Generalizing our results ... 122
5.2.1. Foreign currency forward contracts ... 124
5.2.2. Commodity forward contracts ... 125
5.2.3. Counterparty risk in forward contracts ... 130
5.3. Futures contracts ... 131
5.3.1. Counterparty risk with futures contracts ... 133
5.3.2. A brief history of financial futures ... 134
5.3.3. Cash versus physical delivery ... 135
5.3.4. Futures positions in practice ... 137
5.4. How to lose money on futures and forward contracts ... 139
5.4.1. Pricing futures contracts ... 139
5.4.2. The role of the expected future spot price ... 143
5.4.3. The impact of financial market imperfections ... 145
5.5. Summary ... 146
Key Concepts ... 147
Review Questions ... 147
Questions and Exercises ... 147
Literature Note ... 149
Chapter 6 Hedging Exposures with Forward and Futures Contracts ... 151
6.1. Measuring risk : Volatility, CaR, and VaR ... 152
6.2. Hedging when there is no basis risk ... 156
6.3. Hedging when the basis is not zero ... 160
6.3.1. The volatility-minimizing hedge when there is a deterministic relation between the futures price and the spot price ... 161
6.3.2. Hedging when the basis is random ... 165
6.3.3. The volatility-minimizing hedge and regression analysis ... 171
6.3.4. The effectiveness of the hedge ... 176
6.4. Putting it all together in an example ... 179
6.5. Hedging when returns rather than level changes are i.i.d. ... 182
6.6. Summary ... 184
Key Concepts ... 185
Review Questions ... 185
Questions and Exercises ... 186
Literature Note ... 187
Chapter 7 Optimal Hedges for the Real World ... 189
7.1. Implementing the minimum-variance hedge in the real world ... 191
7.1.1. Hedging, contract maturity, and basis risk ... 191
7.1.2. Basis risk, the hedge ratio, and contract maturity ... 193
7.1.3. Cross-hedging ... 195
7.1.4. Liquidity ... 195
7.1.5. Imperfect divisibility ... 196
7.1.6. The multivariate normal changes model : Cash versus futures prices ... 197
7.2. The costs of hedging ... 199
7.3. Multiple exposures with same maturity ... 208
7.4. Cash flows occurring at different dates ... 212
7.5. Metallgesellschaft ... 215
7.6. Summary ... 219
Key Concepts ... 220
Review Questions ... 220
Questions and Exercises ... 220
Literature Note ... 221
Chapter 8 Identifying and Managing Cash Flow Exposures ... 223
8.1. Price and quantity risks ... 225
8.1.1. Risky foreign currency cash flows ... 225
8.1.2. Optimal hedges with quantity risk ... 227
8.2. The exposures of Motor Inc. ... 229
8.2.1. Cash flow exposure and time horizon ... 231
8.2.2. Competitive exposures ... 231
8.3. Using the pro forma statement to evaluate exposures ... 235
8.4. Modeling cash flow exposures ... 236
8.5. Using regression analysis to measure exposure ... 244
8.6. Monte Carlo approaches ... 247
8.7. Hedging competitive exposures ... 252
8.8. Summary ... 253
Key Concepts ... 254
Review Questions ... 254
Questions and Exercises ... 255
Literature Note ... 256
Chapter 9 Measuring and Managing Interest Rate Risks ... 257
9.1. Debt service and interest rate risks ... 258
9.1.1. Optimal floating and fixed rate debt mix ... 258
9.1.2. Hedging debt service with the eurodollar futures contract ... 259
9.1.3. Forward rate agreements ... 265
9.2. The interest rate exposure of cash flow and earnings for financial institutions ... 265
9.3. Measuring and hedging interest rate exposures ... 271
9.3.1. Measuring yield exposure ... 273
9.3.2. Improving on traditional duration ... 278
9.4. Measuring and managing interest rate risk without duration ... 286
9.4.1. Using zero-coupon bond prices as risk factors ... 288
9.4.2. Reducing the number of sources of risk : Factor models ... 289
9.4.3. Forward curve models ... 292
9.5. Summary ... 295
Key Concepts ... 296
Review Questions ... 296
Questions and Exercises ... 297
Literature Note ... 298
Chapter 10 Hedging with Options ... 299
10.1. Using options to create static hedges ... 301
10.1.1. Options as investment insurance contracts ... 301
10.1.2. Options as exchange rate insurance contracts, The case of Export Inc. ... 303
10.1.3. Options to hedge contingent exposures ... 308
10.1.4. How we can hedge(almost) anything with options ... 310
10.2. A brief history of option markets ... 314
10.3. Some properties of options ... 315
10.3.1. Upper and lower bounds on option prices ... 315
10.3.2. Exercise price and option values ... 317
10.3.3. The value of options and time to maturity ... 319
10.3.4. Put-call parity theorem ... 319
10.3.5. Option values and cash payouts ... 321
10.3.6. American options and put-call parity ... 323
10.4. Summary ... 324
Key Concepts ... 325
Review Questions ... 325
Questions and Exercises ... 325
Literature Note ... 327
Chapter 11 Option Pricing, Dynamic Hedging, and the Binomial Model ... 329
11.1. Arbitrage pricing and the binomial model ... 331
11.1.1. The replicating portfolio approach to price an option ... 331
11.1.2. Pricing options by constructing a hedge ... 333
11.1.3. Why the stock's expected return does not affect the option price ... 334
11.1.4. The binomial model ... 335
11.2. The binomial approach with multiple periods ... 339
11.2.1. The binomial approach with two periods ... 339
11.2.2. Pricing a European option that matures in n periods ... 345
11.3. The binomial model and early exercise ... 347
11.3.1. Using the binomial approach to price a European call on a dividend paying stock ... 347
11.3.2. Using the binomial approach to price an American call on a dividend paying stock ... 350
11.3.3. Using the binomial approach to price American puts ... 351
11.4. Back to hedging everything and anything ... 352
11.5. Summary ... 355
Key Concepts ... 356
Review Questions ... 356
Questions and Exercises ... 356
Literature Note ... 357
Chapter 12 The Black-Scholes Model ... 359
12.1. The Black-Scholes model ... 360
12.2. The determinants of the call option price ... 367
12.3. Extensions and limitations of the Black-Scholes formula ... 374
12.3.1. Pricing puts ... 374
12.3.2. Taking dividends into account ... 377
12.3.3. What if volatility changes over time? ... 379
12.3.4. What if the option is an American option? ... 382
12.3.5. What if the stock price is not distributed lognormally? ... 383
12.4. Empirical evidence on the pricing of options on stocks ... 385
12.5. Beyond plain vanilla Black-Scholes ... 387
12.5.1. Pricing currency and futures options ... 389
12.5.2. The Monte Carlo approach ... 391
12.6. Summary ... 392
Key Concepts ... 392
Review Questions ... 393
Questions and Exercises ... 393
Literature Note ... 394
Chapter 13 Risk Measurement and Risk Management with Nonlinear Payoffs ... 397
13.1. Estimating the risk of nonlinear payoffs using delta ... 398
13.1.1. The risk of an option : The delta-VaR method ... 399
13.1.2. The risk of a portfolio of options written on the same stock ... 402
13.1.3. The risk of a portfolio of options written on different underlying assets ... 402
13.2. Beyond delta-VaR ... 404
13.2.1. Measuring the risk of a portfolio of options over longer periods of time ... 404
13.2.2. Alternative methods to computing the VaR of an option or portfolio of options ... 407
13.2.3. Leeson, Barings, delta-VaR, delta-gamma VaR, and Monte Carlo VaR ... 411
13.2.4. Stress tests ... 416
13.3. Portfolio insurance ... 418
13.4. Using options to hedge quantity risk ... 421
13.5. Summary ... 424
Key Concepts ... 424
Review Questions ... 424
Questions and Exercises ... 425
Literature Note ... 426
Chapter 14 Options on Bonds and Interest Rates ... 427
14.1. Caps and floors ... 430
14.1.1. Hedging with caps ... 430
14.1.2. Pricing caps and floors ... 430
14.2. Hedging with options and measuring the interest rate exposure of bond options ... 435
14.3. Beyond Black-Scholes ... 440
14.3.1. The limitations of the Black-Scholes approach ... 440
14.3.2. Alternate approaches ... 442
14.4. Spot interest rate models ... 443
14.4.1. Building interest rate and bond price trees ... 443
14.4.2. Spot interest rate models and tree building ... 446
14.4.3. Interest rate models and derivatives pricing ... 449
14.4.4. The Vasicek model and risk management ... 452
14.5. Building trees from the forward curve : The Heath-Jarrow-Morton(HJM) model ... 455
14.5.1. The forward rate tree ... 455
14.6. HJM models as periods become shorter ... 456
14.7. Some empirical evidence ... 462
14.8. Summary ... 464
Key Concepts ... 464
Review Questions ... 464
Questions and Exercises ... 465
Literature Note ... 466
Part 3 Beyond Plain Vanilla Risk Management ... 467
Chapter 15 The Demand and Supply for Derivative Products ... 469
15.1. Comparing payoff production technologies ... 472
15.1.1. Exchange-traded option ... 472
15.1.2. Over-the-counter option ... 473
15.1.3. Dynamic replication ... 478
15.1.4. Static replication ... 481
15.1.5. Comparison ... 482
15.2. The suppliers of derivatives ... 482
15.2.1. Exchanges ... 483
15.2.2. Financial intermediaries ... 483
15.2.3. The "do it yourself approach" ... 486
15.3. Financial innovation and financial engineering ... 487
15.3.1. The life-cycle of financial products ... 487
15.3.2. The profits from innovation ... 489
15.4. Embedded derivatives ... 490
15.4.1. Bundling can reduce credit risks associated with the issuer's debt ... 493
15.4.2. Bundling can offer new investment opportunities to investors ... 493
15.4.3. Bundling can eliminate difficulties with counterparties ... 493
15.4.4. Bundling can reduce transaction costs ... 493
15.5. Assessing the trade-offs ... 494
15.6. Summary ... 495
Key Concepts ... 495
Review Questions ... 495
Questions and Exercises ... 496
Literature Note ... 497
Chapter 16 Swaps ... 499
16.1. The swap market and its evolution ... 501
16.2. Interest rate swaps ... 505
16.2.1. Pricing a new swap ... 506
16.2.2. Pricing an outstanding swap ... 510
16.2.3. Measuring the risk of an interest rate swap ... 513
16.2.4. Do swaps make something out of nothing? ... 514
16.3. Beyond simple interest rate swaps ... 517
16.3.1. Pricing, risk evaluation, and hedging currency swaps ... 517
16.3.2. Swaps where the notional amount changes over time ... 520
16.3.3. Total return swaps ... 522
16.3.4. Swaps with options ... 523
16.3.5. Forwards and options on swaps ... 524
16.4. Case study : The Procter & Gamble levered swap ... 526
16.5. Summary ... 529
Key Concepts ... 530
Review Questions ... 530
Questions and Exercises ... 531
Literature Note ... 532
Chapter 17 Using Exotic Options ... 533
17.1. Digital options ... 535
17.2. Barrier options ... 539
17.2.1. Why use barrier options? ... 540
17.2.2. Pricing and hedging barrier options ... 543
17.2.3. Some surprising properties of barrier options ... 544
17.2.4. Some practical issues ... 548
17.3. Options on the average ... 550
17.3.1. A binomial example of an option on the average ... 551
17.3.2. A replicating portfolio for the average ... 551
17.3.3. Pricing options on the average using the Monte Carlo approach ... 553
17.3.4. Evaluation of options on the average during the averaging interval ... 558
17.4. Options on multiple assets ... 559
17.4.1. Basket options ... 559
17.4.2. Quantos ... 560
17.4.3. Exchange options ... 561
17.5. Risk management and exotic options : The lessons from Gibson Greetings Inc. ... 563
17.6. Summary ... 566
Key Concepts ... 567
Review Questions ... 567
Questions and Exercises ... 567
Literature Note ... 569
Chapter 18 Credit Risks and Credit Derivatives ... 571
18.1. Credit risks as options ... 572
18.1.1. Finding firm value and firm value volatility ... 576
18.1.2. Pricing the debt of In-The-Mail Inc. ... 578
18.1.3. Subordinated debt ... 580
18.1.4. The pricing of debt when interest rates change randomly ... 582
18.1.5. VaR and credit risks ... 585
18.2. Beyond the Merton model ... 586
18.3. Credit risk models ... 588
18.3.1. CreditRisk+ ... 590
18.3.2. CreditMetric<?import namespace ... m ur
18.3.3. The KMV model ... 595
18.3.4. Some difficulties with credit portfolio models ... 596
18.4. Credit derivatives ... 596
18.5. Credit risks of derivatives ... 599
18.6. Summary ... 601
Key Concepts ... 601
Review Questions ... 601
Questions and Exercises ... 602
Literature Note ... 603
Chapter 19 Recent Developments in the Practice of Risk Management ... 605
19.1. Long-Term Capital Management(LTCM) ... 606
19.2. The operational risk of risk management ... 611
19.2.1. Steps in implementation of VaR ... 611
19.2.2. What can go wrong with implementation? ... 612
19.3. Is it the right risk measure? ... 617
19.3.1. VaR diagnostics ... 617
19.3.2. Fat tails and the distribution of extreme returns ... 621
19.3.3. Alternative risk measures ... 624
19.3.4. Measuring operational risk ... 626
19.4. The current regulatory environment ... 627
19.4.1. SFAS 133 ... 627
19.4.2. Disclosure ... 630
19.5. Empirical evidence on risk management practice ... 630
19.5.1. The survey evidence ... 631
19.5.2. Studies relating derivatives usage to firm characteristics ... 632
19.5.3. Risk management, risk, and value ... 637
19.6. Summary ... 638
Key Concepts ... 638
Review Questions ... 638
Questions and Exercises ... 639
Literature Note ... 640
Part 4 Conclusion ... 641
Epilogue ... 643
Glossary ... 645
Bibliography ... 653
Index ... 663
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