About the Authors xxvii

About the Companion Site xxix

Preface xxxi

Chapter 1 Derivative Securities 1

1.1 Forwards and Futures 2

1.2 Options 7

1.3 Swaps 14

1.4 Hedging, Speculation, and Arbitrage 16

1.5 Short-Selling 18

1.6 Summary 20

Exercises 21

Part I Forwards and Futures 23

Chapter 2 Futures Markets 25

2.1 Trading on Futures Markets 25

2.2 Futures Exchanges and Traders 29

2.3 Margins and Marking-to-Market 30

2.4 Summary 36

Exercises 36

Chapter 3 Forward and Futures Prices 39

3.1 Pricing Forward Contracts 39

3.2 Dividends, Storage Costs, and Convenience Yield 46

3.3 Commodity Futures 49

3.4 Value of a Forward Contract 53

3.5 Summary 57

Exercises 57

Chapter 4 Futures: Hedging and Speculation 59

4.1 Hedging Using Futures 59

4.2 Novel Futures Contracts 67

4.3 Speculation 70

4.4 Summary 72

Exercises 73

Chapter 5 Index Futures 75

5.1 Stock Index Futures (SIF) 76

5.2 Index Arbitrage 78

5.3 Hedging 81

5.4 Tailing the Hedge 88

5.5 Summary 89

Appendix 5: Hedge Ratios 89

Exercises 93

Chapter 6 Strategies: Stock Index Futures 95

6.1 Underpriced Stocks: Hedging Market Risk 95

6.2 Overpriced Stocks: Hedging Market Risk 98

6.3 Market-neutral Hedge Fund 100

6.4 Long-Short Hedge Fund 101

6.5 Changing Stock Market Exposure 104

6.6 Merger Arbitrage 106

6.7 Summary 109

Appendix 6.A: Stock Picking and Market Risk 110

Appendix 6.B: Market Timing 112

Appendix 6.C: Hedging: Long-Short Portfolio 114

Appendix 6.D: Merger Arbitrage and Hedging 116

Exercises 117

Chapter 7 Currency Forwards and Futures 119

7.1 FX-Futures Contracts 120

7.2 Pricing FX-Forward Contracts 123

7.3 Pricing FX-Futures Contracts 126

7.4 Hedging and Speculation: Forwards 127

7.5 Hedging and Speculation: Futures 129

7.6 Summary 132

Appendix 7: Hedging Using FX-Futures 133

Exercises 135

Part II Fixed Income: Cash Markets 137

Chapter 8 Interest Rates 139

8.1 LIBOR, Repos, Fed Funds, and OIS Rates 139

8.2 Day-Count Conventions 141

8.3 Forward Rates 146

8.4 Forward Rate Agreements (FRAs) 150

8.5 Summary 154

Exercises 154

Chapter 9 Bond Markets 157

9.1 Prices, Yields, and Return 158

9.2 Pricing Coupon Bonds 165

9.3 Summary 168

Exercises 169

Chapter 10 Bonds: Duration and Convexity 171

10.1 Yield Curve 171

10.2 Duration and Convexity 173

10.3 Summary 178

Appendix 10: Duration and Convexity 179

Exercises 181

Part III Fixed Income Futures Contracts 183

Chapter 11 Interest Rate Futures 185

11.1 Three-month Eurodollar Futures Contract 186

11.2 Sterling 3-month Futures Contract 188

11.3 T-bill Futures 188

11.4 Futures Price and Forward Rates 189

11.5 Pricing Interest Rate Futures 190

11.6 Arbitrage: Implied Repo Rate 193

11.7 Speculation 195

11.8 Spread Trades 196

11.9 Summary 199

Appendix 11.A: Futures Prices and Interest Rates 200

Exercises 203

Chapter 12 Hedging with Interest Rate Futures 205

12.1 Number of Futures Contracts 206

12.2 Different Types of Hedge 210

12.3 Hedging: T-bill and Eurodollar Futures 214

12.4 Eurodollar Stack Hedge 217

12.5 Summary 221

Appendix 12: Hedge Ratios 222

Exercises 224

Chapter 13 T-bond Futures 227

13.1 Contract Specifications 228

13.2 Conversion Factor and Cheapest-to-Deliver 230

13.3 Hedging Using T-Bonds 234

13.4 Hedging: Further Issues 235

13.5 Market Timing 238

13.6 Wild Card Play 239

13.7 Pricing T-bond Futures 240

13.8 T-bond Futures Spreads 244

13.9 Summary 247

Appendix 13.A: Hedging: Duration and Market Timing 248

Appendix 13.B: Implied Repo Rate and Arbitrage 250

Exercises 251

Part IV Options 253

Chapter 14 Options Markets 255

14.1 Market Organisation 255

14.2 Call Options 261

14.3 Put Options 268

14.4 Intrinsic Value and Time Value 273

14.5 Summary 276

Exercises 277

Chapter 15 Uses of Options 279

15.1 Protective Put 279

15.2 Put–Call Parity: European Options 282

15.3 Guaranteed Bond 283

15.4 Other Options 286

15.5 Summary 288

Exercises 289

Chapter 16 Black–Scholes Model 291

16.1 Determinants of Option Prices 291

16.2 Black–Scholes 296

16.3 Are Stocks Less Risky in the Long Run? 303

16.4 Delta Hedging 306

16.5 Implied Volatility 308

16.6 Summary 311

Appendix 16: Price Bounds on European Options 312

Exercises 313

Chapter 17 Option Strategies 315

17.1 Synthetic Securities 316

17.2 Bull and Bear Spreads 320

17.3 Straddle, Strangle, Butterfly, and Condor 324

17.4 Horizontal (Time, Calendar) Spreads 333

17.5 Summary 335

Exercises 335

Chapter 18 Stock Options and Stock Index Options 337

18.1 Options on Stocks 337

18.2 Stock Index Options (SIO) 342

18.3 Summary 345

Appendix 18.A: Static Hedge: Index Puts 345

Appendix 18.B: Dynamic Delta Hedge 346

Exercises 346

Chapter 19 Foreign Currency Options 349

19.1 Contract Specifications 349

19.2 Speculation 350

19.3 Hedging Foreign Currency Exposure 353

19.4 Other Currency Options 358

19.5 Summary 358

Exercises 359

Chapter 20 Options on Futures 363

20.1 Market Conventions 363

20.2 Price Bounds on European Futures Options 366

20.3 Trading Strategies 367

20.4 Summary 370

Exercises 371

Part V Options Pricing 373

Chapter 21 BOPM: Introduction 375

21.1 One-Period BOPM 375

21.2 Risk-neutral Valuation 379

21.3 Determinants of Call Premium 382

21.4 Pricing a European Put Option 383

21.5 Summary 384

Appendix 21: No-arbitrage Conditions 385

Exercises 386

Chapter 22 BOPM: Implementation 389

22.1 Generalising the BOPM 390

22.2 Replication Portfolio 393

22.3 BOPM to Black–Scholes 396

22.4 Summary 398

Appendix 22: Delta Hedging and Arbitrage 399

Exercises 402

Chapter 23 BOPM: Extensions 405

23.1 American Options 405

23.2 Options on Other Underlying Assets 407

23.3 Options on Futures Contracts 409

23.4 Options on Dividend-paying Stocks 412

23.5 Summary 414

Appendix 23: BOPM and Risk-neutral Valuation 415

Exercises 419

Chapter 24 Analysis of Black–Scholes 421

24.1 Volatility 421

24.2 Testing Black–Scholes 425

24.3 Limitations of Black–Scholes 428

24.4 Summary 431

Exercises 432

Chapter 25 Pricing European Options 435

25.1 What do N(d1) and N(d2) Represent? 435

25.2 European Options: Dividend Paying Stocks 436

25.3 Foreign Currency and Futures Options 437

25.4 Put–Call Parity 440

25.5 Summary 443

Exercises 444

Chapter 26 Pricing Options: Monte Carlo Simulation 447

26.1 Brownian Motion: Parallel Universe 447

26.2 Pricing a European Call 449

26.3 Variance Reduction Methods 454

26.4 The Greeks 455

26.5 Multiple Stochastic Factors 456

26.6 Path-dependent Options 459

26.7 Summary 460

Appendix 26: MCS, Several Stochastic Variables 461

Exercises 464

Part VI The Greeks 467

Chapter 27 Delta Hedging 469

27.1 Delta 469

27.2 Dynamic Delta Hedging 473

27.3 Summary 481

Exercises 481

Chapter 28 The Greeks 483

28.1 Different Greeks 483

28.2 Hedging with the Greeks 491

28.3 Greeks and the BOPM 496

28.4 Summary 498

Appendix 28: Black–Scholes and the Greeks 499

Exercises 502

Chapter 29 Portfolio Insurance 503

29.1 Static Hedge 504

29.2 Dynamic Portfolio Insurance 507

29.3 Summary 513

Exercises 514

Part VII Advanced Options 517

Chapter 30 Other Options 519

30.1 Corporate Equity and Debt 519

30.2 Warrants 522

30.3 Equity Collar 524

30.4 Summary 526

Exercises 527

Chapter 31 Exotic Options 529

31.1 Three-period BOPM 530

31.2 Asian Options 531

31.3 Other Exotics: Lookbacks, Barrier, Compound, and Chooser 535

31.4 Summary 542

Exercises 543

Chapter 32 Energy and Weather Derivatives 545

32.1 Energy Contracts 546

32.2 Hedging with Energy Futures 549

32.3 Energy Swaps 552

32.4 Weather Derivatives 557

32.5 Reinsurance and CAT Bonds 562

32.6 Summary 562

Exercises 563

Part VIII Swaps 567

Chapter 33 Interest Rate Swaps 569

33.1 Using Interest Rate Swaps 571

33.2 Cash Flows in a Swap 573

33.3 Settlement and Price Quotes 575

33.4 Terminating a Swap 577

33.5 Comparative Advantage 577

33.6 Summary 581

Appendix 33: Comparative Advantage with Swap Dealer 581

Exercises 583

Chapter 34 Pricing Interest Rate Swaps 585

34.1 Cash Flows in a Swap 586

34.2 Floating Rate Note (FRN) 587

34.3 Pricing a Swap: Short Method 589

34.4 Pricing a Swap: Forward Rate Method 591

34.5 Market Value of a Swap 593

34.6 Swap Delta and PVBP 596

34.7 Summary 597

Appendix 34: Value of an FRN Using Arbitrage 597

Exercises 598

Chapter 35 Other Interest Rate Swaps 601

35.1 Swap Deals 601

35.2 Pricing Non-standard Swaps 603

35.3 Hedging Interest Rate Swaps 608

35.4 Credit Risk 614

35.5 Summary 615

Exercises 616

Chapter 36 Currency Swaps 617

36.1 Uses 617

36.2 Pricing a Fixed-Fixed Currency Swap 620

36.3 Valuing a Fixed-Fixed Currency Swap 622

36.4 Summary 625

Appendix 36.A: Pricing a Currency Swap 626

Appendix 36.B: Valuation of a Currency Swap 628

Exercises 629

Chapter 37 Equity Swaps 631

37.1 Equity-for-LIBOR: Fixed Notional Principal 632

37.2 Unhedged Cross-currency Equity Swap 634

37.3 Hedged Cross-currency Equity Swap 635

37.4 Pricing Equity Swaps 636

37.5 Summary 643

Appendix 37: Valuation of Equity-for-LIBOR Swap 643

Exercises 644

Part IX Fixed Income Derivatives 647

Chapter 38 T-Bond Option, Caps, Floors and Collar 649

38.1 Options on T-Bonds and Eurodollars 649

38.2 Caplets and Floorlets 650

38.3 Interest Rate Cap 655

38.4 Interest Rate Floor 657

38.5 Interest Rate Collar 658

38.6 Summary 661

Exercises 662

Chapter 39 Swaptions, Forward Swaps, and MBS 665

39.1 Swaptions 665

39.2 Forward Swaps 668

39.3 Mortgage-backed Securities (MBS) 670

39.4 Hedging Fixed Income Derivatives 675

39.5 Summary 677

Exercises 678

Chapter 40 Pricing Fixed Income Options: Black’s Model and MCS 681

40.1 Black’s Model: European Options 682

40.2 Pricing a Caplet Using MCS 684

40.3 European Swaption: Black’s Model 685

40.4 Summary 688

Exercises 688

Chapter 41 Pricing Fixed Income Derivatives: BOPM 691

41.1 No-arbitrage Approach: BOPM 692

41.2 Pricing a Coupon Bond 697

41.3 Pricing Options 697

41.4 Pricing a Callable Bond 700

41.5 Pricing Caps 701

41.6 Pricing FRAs 702

41.7 Pricing a Swaption 704

41.8 Pricing FRNs with Embedded Options 705

41.9 More Lattices 708

41.10 Summary 709

Exercises 710

Part X Credit Derivatives 713

Chapter 42 Credit Default Swaps (CDS) 715

42.1 Credit Risk and CDS 716

42.2 Speculation with CDS 717

42.3 Contract Details 719

42.4 Pricing and Valuation 720

42.5 Bond Yields and the CDS Spread 725

42.6 Credit Indices and other CDS Contracts 727

42.7 Derivatives on the CDS Spread 727

42.8 Summary 729

Exercises 730

Chapter 43 Securitisation, ABSs and CDOs 731

43.1 ABSs and ABS-CDOs 731

43.2 Credit Enhancement 736

43.3 Losses on ABSs and ABS-CDOs 738

43.4 Sub-prime Crisis 2007–8 740

43.5 Synthetic CDOs 743

43.6 Single Tranche Trading 744

43.7 Total Return Swap 746

43.8 Summary 747

Exercises 748

Part XI Market Risk 749

Chapter 44 Value at Risk 751

44.1 Introduction 751

44.2 Value at Risk (VaR) 752

44.3 Forecasting Volatility 761

44.4 Backtesting 763

44.5 Capital Adequacy 766

44.6 Summary 767

Exercises 768

Chapter 45 VaR: Other Portfolios 769

45.1 Single Index Model 769

45.2 VaR for Coupon Bonds 773

45.3 VaR: Options 777

45.4 Summary 779

Appendix 45.A: VaR for Foreign Assets 779

Appendix 45.B: Single Index Model (SIM) 780

Appendix 45.C: Cash Flow Mapping 782

Exercises 784

Chapter 46 VaR: Alternative Measures 787

46.1 Historical Simulation 787

46.2 Bootstrapping 792

46.3 Monte Carlo Simulation 795

46.4 Alternative Methods 799

46.5 Summary 803

Exercises 804

Part XII Price Dynamics 807

Chapter 47 Asset Price Dynamics 809

47.1 Stochastic Processes 810

47.2 Geometric Brownian Motion (GBM) and Ito’s Lemma 812

47.3 Distribution of Log Stock Price and Stock Price 814

47.4 Summary 817

Appendix 47: Ito’s Lemma 817

Exercises 818

Chapter 48 Black–Scholes PDE 821

48.1 Risk-Neutral Valuation and Black–Scholes PDE 821

48.2 Finite Difference Methods 826

48.3 Summary 830

Appendix 48: Derivation of Black–Scholes PDE 830

Exercises 833

Chapter 49 Equilibrium Models: Term Structure 835

49.1 Risk-neutral Valuation 836

49.2 Models of the Short-Rate 837

49.3 Pricing Using Continuous Time Models 839

49.4 Bond Prices and Derivative Prices 841

49.5 Summary 843

Exercises 844

Glossary 845

Bibliography 867

Author Index 871

Subject Index 873