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

Three experts provide an authoritative guide to the theory and practice of derivatives Derivatives: Theory and Practice and its companion website explore the practical uses of derivatives and offer a guide to the key results on pricing, hedging and speculation using derivative securities. The book links the theoretical and practical aspects of derivatives in one volume whilst keeping mathematics and statistics to a minimum. Throughout the book, the authors put the focus on explanations and applications. Designed as an engaging resource, the book contains commentaries that make serious points in a lighthearted manner. The authors examine the real world of derivatives finance and include discussions on a wide range of topics such as the use of derivatives by hedge funds and the application of strip and stack hedges by corporates, while providing an analysis of how risky the stock market can be for long-term investors, and more. To enhance learning, each chapter contains learning objectives, worked examples, details of relevant finance blogs technical appendices and exercises.