0_Contents - CONTENTS IN BRIEF List of Business Snapshots

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Unformatted text preview: CONTENTS IN BRIEF List of Business Snapshots ........................................................................ .. xvi List of Technical Notes ............................................................................ .. xvii Preface ..................................................................................................... .. xix “1. Introduction ................................................................................................ ..1 V 2. Mechanics of futures markets ..................................................................... ..21 " 3. Hedging. strategies using futures .................................................................. ..47 " 4. Interest rates ............................................................................................. .. 75 V 5. Determination of forward and futures prices ............................................... ..99 " 6. Interest rate futures .................................................................................. .. 129 V/ 7. Swaps ..................................................................................................... .. 149 x/ 8.\Mechanics of options markets .................................................................. .. 181 V 9. Properties of stock options ....................................................................... .. 205 V 10. Trading strategies involving options ........................................................... .223 v’ 11. Binomial trees ......................................................................................... .. 241 V 12. Wiener processes and Ito’s lemma ............................................................. .. 263 x/ 13. The Black—Scholes—Merton model ................. .., ....................................... .. 281 w 14. Options on stock indices, currencies, and futures ....................................... .. 313 v 15. The Greek letters ............................................................ ....................... .. 341 v 16. Volatility smiles ................................... .................................................. .. 375 17. Basic numerical procedures ...................................................................... .. 391 V18. Value at risk ........................................................................................... .. 43S 19. Estimating v01atilities and correlations ....................................................... .. 461 20. Credit risk .............................................................................................. .. 481 21. Credit derivatives ..................................................................................... .. 507 22. Exotic options ......................................................................................... .. 529 23. Weather, energy, and insurance derivatives ................................................ .. 551 24. More on models and numerical pIOCedures ................................................ .. 561 25. Martingales and measures ........................................................................ .. 589 26. Interest rate derivatives: the standard market models .................................. .. 611 27. Convexity, timing, and quanto adjustments ............................................. 635 28. Interest rate derivatives: models of the short rate ........................................ .. 649 29. Interest rate derivatives: HIM and LMM .................................................. .. 679 30. Swaps revisited ........................................................................................ .. 697 31. Real Options ........................................................................................... .. 713 V 32. Derivatives mishaps and what we can learn from them ............................... .. 729 Glossary of terms .................................................................................... .. 741 DerivaGem software ................................................................................ .. 761 Major exchanges trading futures and options ............................................. .. 767 Tables for N(x) ....................................................................................... .. 768 Author index .......................................................................... .. ............... .. 771 Subject index ........................................................................................... .. 775 Chapter 1 Chapter 2 Chapter 3 Contents List of Business Snapshots ............................................................................. ..xvi List of Technical Notes ................................................................................ ..vaii Preface ..................................................................................................... .. xix Introduction .................................................................................................. .. 1 1.1 Exchange~traded markets ...................................................................... .. 1 1.2 Over—the-counter markets ...................................................................... .. 2 1.3 Forward contracts ...................................... ........................................ .. 3 1.4 ' Futures contracts ................................................................................. .. 6 1.5 Options ..................... ............................................. ........................ .. 6 1.6 Types of traders ................................................................................... .. 8 1.7 Hedgers .............................................................................................. .. 9 1.8 Speculators ....................................................................................... .. 11 1.9 Arbitrageurs ...................................................................................... .. 14 1.10 Dangers ........................................................................................... .. 15 Summary ............................................... ......................................... .. 15 Further reading ................................................................................. .. 16 Questions and problems .................................................. .................. .. 16 Assignment questions ......................................................................... .. l8 Mechanics of futures markets ......................................................................... .. 21 2.1 Background ...................................................................................... .. 21 2.2 Specification of a futures contract ........ ............................................... .. 23 2.3 Convergence of futures price to spot price ............... .; ............................ .. 26 2.4 Daily settlement and margins .............................................................. .. 26 2.5 Newspaper quotes ........................................... ................................ .. 31 2.6 Delivery ........................................................................................... .. 35 2.7 Types of traders and types of orders ..................................................... .. 36 2.8 Regulation ........................................................................................ .. 37 2.9 Accounting and tax ............................................................................ .. 39 2.10 Forward vs. futures contracts ............................................................... .. 40 Summary .......................................................................................... .. 41 Further reading ................................................................................. .. 42 Questions and problems ...................................................................... .. 43 Assignment questions ......................................................................... .. 44 Hedging strategies using futures ...................................................................... .. 47 3.1 Basic principles .................................................................................. .. 47 3.2 Arguments for and against hedging ...................................................... .. 50 3.3 Basis risk .......................................................................................... .. 53 3.4 Cross hedging ................................................................................... .. 56 3.5 Stock index futures ....................................... ..Z .................................. .. 60 vii viii Contents 3.6 Rolling the hedge forward ................................................................... .. 67 Summary .......................................................................................... .. 68 Further reading .................................................................................. .. 69 Questions and problems ...................................................................... .. 70 Assignment questions .......................................................................... .. 71 Appendix: Proof of the minimum variance hedge ratio formula ................ .. 73 Chapter 4 Interest rates ............................................................................................... .. 75 4.1 Types of rates .................................................................................... .. 75 4.2 Measuring interest rates ...................................................................... .. 77 4.3 Zero rates ......................................................................................... .. 80 4.4 Bond pricing ................................................................... .. ................ .. 80 4.5 Determining Treasury zero rates ........................................................... .. 82 4.6 Forward rates .................................................................................... .. 84 ‘47 Forward rate agreements ..................................................................... .. 87 4.8 Duration ........................................................................................... .. 89 4.9 Convexity .......................................................................................... .. 92 4.10 Theories of the term structure of interest rates ........................................ .. 93 Summary .......................................................................................... .. 94 Further reading .................................................................................. .. 95 Questions and problems ...................................................................... .. 95 Assignment questions .......................................................................... .. 97 Chapter 5 Determination of forward and futures prices: .................................................... .. 99 5.1' v Investment assets vs. consumption assets ............................................... .. 99 5.2 Short selling ...................................................................................... .. 99 5.3 Assumptions and notation ................................................................. .. 101 54 Forward price for an investment asset ................................................. .. 101 5.5 Known income ................................................................................ .. 104 5.6 Known yield .................................................................................... .. 107 5.7 Valuing forward contracts ................................................................. .. 107 5.8 Are forward prices and futures prices equal? ........................................ .. 109 5.9 Futures prices of stock indices ............................................................ .. 110 5.10 Forward and futures contracts on currencies ............................... ...... .. 112 5.11 Futures on commodities .................................................................... .. 116 5.12 The cost of carry .............................................................................. .. 118 5.13 Delivery options ............................................................................... .. 119 5.14 Futures prices and expected future spot prices ...................................... .. 119 Summary ........................................................................................ .. 121 Further reading ................................................................................ .. 122 Questions and problems .................................................................... .. 123 Assignment questions ........................................................................ .. 125 Appendix: Proof that forward and futures prices are equal when interest A rates are constant .............................................................. .. 127 Chapter 6 Interest rate futures .................................................................................... .. 129 6.1 Day count conventions ................................................... .. ................ .. 129 6.2 Quotations for Treasury bonds ........................................................... .. 131 6.3 Treasury bond futures ....................................................................... .. 133 6.4 Eurodollar futures ............................................................................ .. 137 6.5 Duration—based hedging strategies ....................................................... .. 142 6.6 Hedging portfolios of assets and liabilities ........................................... .. 143 Summary ........................................................................................ .. 144 Contents ix Further reading ................................................................................. .. 145 Questions and problems ........................................ ..5 .......................... .. 145 Assignment questions .......................................... ..L'. .......................... .. 147 Chapter 7 Swaps ........................................................................... ... ......................... .. 149 7.1 Mechanics of interest rate swaps ......................................................... .. 149 7.2 Day count issues ............................................... ... ............................. .. 155 7.3 Confirmations ................................................... .: ............................. .. 156 7.4 The comparative~advantage argument .................................................. .. 157 7.5 The nature of swap rates .................................................................... .. 160 7.6 Determining the LIBOR/swap zero rates .............................................. .. 160 7.7 Valuation of interest rate swaps ........................................................... .. 161 7.8 Currency swaps ................................................................................ .. 165 7.9 Valuation of currency swaps ............................................................... .. 168 7.10 Credit risk ....................................................................................... .. 171 7.11 Other types of swaps ......................................................................... .. 173 Summary ......................................................................................... .. 175 Further reading ................................................. ..~ ............................. .. 176 Questions and problems ..................................................................... .. 176 Assignment questions ........................................................................ .. 178 Chapter 8 Mechanics of options markets ....................................................................... .. 181 8.1 Types of options .............................. ..' ............................................... .. 181 8.2 Option positions ............................................................................... .. 183 8.3 Underlying assets .............................................................................. .. 185 8.4 Specification of stock options ............................................................. .. 187 8.5 Newspaper quotes ............................................................................. .. 190 8.6 Trading ........................................................................................... .. 192 8.7 Commissions .................................................................................... .. 192 8.8 Margins ................................................................ ........................ .. 194 8.9 The options clearing corporation; ....................................................... .. 195 8.10 Regulation ....................................................................................... .. 196 8.11 Taxation .......................................................................................... .. 196 8.12 Warrants,'executive stock options, and convertibles ................................ .. 197 8.13 Over—the~counter markets ................................................................... .. 198 Summary ......................................................................................... ..200 Further reading ................................................................................ .. 200 Questions and problems ..................................................................... ..201 Assignment questions ........................................................................ .. 202 Chapter 9 Properties of stock options ........................................................................... ..205 9.1 Factors aiTecting option prices ............................................................ ..205 9.2 Assumptions and notation ................................................................. ..209 9.3 Upper and lower bounds for option prices ............................................ ..209 9.4 Put—call parity ................................................................................. .. 212 9.5 Early exercise: calls on a non~dividend~paying stock ............................... ..215 9.6 Early exercise: puts on a non~dividend-paying stock ............................... ..216 9.7 Effect of dividends ............................................................................ .. 218 Summary ......................................................................................... ..219 Further reading ................................................................................. .220 Questions and problems ...................................................................... .220 Assignment questions ......................................................................... .222 Chapter 10 Trading strategies involving options ..................... ......................................... ..223 10.1 Strategies involving a single option and a stock ...................................... .223 X Contents 102 Spreads ............................................................................................ . 225 10.3 Combinations .................................................................................. .. 234 10.4 Other payoffs ................................................................................... .. 237 Summary ........................................................................................ .. 237 Further reading... ............................................................................ .. 238 Questions and problems .................................................................... .. 238 Assignment questions ........................................................................ .. 239 Chapter 11 Binomial trees ........................................................................................... .. 241 11.1 One—step binomial model ................................................................... .. 241 11.2 Risk-neutral valuation ....................................................................... .. 244 11.3 Two-step binomial trees .................................................................... .. 247 11.4 A put example ................................. .................................. .......... .. 249 11.5 American options ............................................................................. .. 250 11.6 Delta .............................................................................................. .. 251 11.7 Matching volatility with u and d ........................................................ .. 252 11.8 Increasing the number of steps ........................................................... .. 255 11.9 Options on other assets ..................................................................... .. 256 Summary ........................................................................................ .. 260 Further reading ................................................................................ .. 260 Questions and problems .................................................................... .. 261 Assignment questions ......................................................................... . 262 Chapter 12 Wiener processes and Ito’s lemma ........................................ ...................... .. 263 12.1 The Markov property ....................................................................... .. 263 12.2 Continuous-time stochastic processesf ................................................. .. 264 12.3 The process for a stock price ............................................................. .. 269 12.4 The parameters ................................................................................. . 272 12.5 Ito’s lemma ..................................................................................... .. 273 12.6 The lognormal property .................................................................... .. 274 Summary ........................................................................................ .. 275 Further reading ................................................................................ .. 276 Questions and problems .................................................................... .. 276 Assigmnent questions ........................................................................ .. 277 Appendix: Derivation of Ito’s lemma .................................................. .. 279 Chapter 13 The Black—Scholes—Merton model ................................................................ .. 281 13.1 .Lognormal property of stock prices .................................................... .. 281 13.2 The distribution of the rate of return .................................................. .. 283 13.3 The expected return .......................................................................... .. 284 13.4 Volatility ......................................................................................... .. 286 13.5 Concepts underlying the Black—Scholes—Merton differential equation ...... .. 289 13.6 Derivation of the Black—Scholes—Merton differential equation ................ .. 291 13.7 Risk-neutral valuation ....................................................................... .. 293 13.8 Black—Scholes pricing formulas .......................................................... .. 295 13.9 Cumulative normal distribution function ............................................. .. 297 13.10 Warrants and executive stock options .................................................. .. 298 13.11 Implied volatilities ........................................................... .._. .............. .. 300 13.12 Dividends ....................................................................................... .. 301 Summary .................................... ................................................. .. 304 Further reading ................................................................................ .. 305 Questions and problems .................................................................... .. 306 Assignment questions ........................................................................ .. 309 Appendix: Proof of Black~Scholes~Merton formula ............................. .. 310 Contents Xi Chapter 14 Options on stock indices, currencies, and futures ............................................... ..313 14.1 Results for a stock paying'a known dividend yield... ......................... ..313 14.2 Option pricing formulas ................................................................ .. 314 14.3 Options on stock indices .................................................................... .. 316 14.4 Currency options .............................................................................. .. 321 14.5 Futures options ................................................................................ ..323 14.6 Valuation of futures options using binomial trees ............................ ..329 14.7 The drift of futures prices in a risk-neutral world .................................. .. 331 14.8 Black’s model for valuing futures options ............................................. ..332 14.9 Futures options vs. spot options ......................................................... ..333 Summary ......................................................................................... .. 334 Further reading ................................................................................ .. 335 Questions and problems ..................................................................... .. 336 Assignment questions ........................................................................ .. 339 Chapter 15 The Greek letters ........................................................................................ ..341 15.1 Illustration ........................................................................... .; .......... .. 341 15.2 Naked and covered positions ................................ ............................ ..342 15.3 A stop-loss strategy ........................................................................... ..342 15.4 Delta hedging ................................................................................... .. 344 15.5 Theta .............................................................................................. ..353 15.6 Gamma ................................................................... ..‘. ..................... ..355 15.7 Relationship between delta, theta, and gamma ...................................... ..359 15.8 Vega ............................................................................................... .. 359 15.9 Rho ................................................................................................ ..362 15.10 The realities of hedging ..................................................................... ..363 15.11 Scenario analysis ............................................................................... ..364 15.12 Portfolio insurance ............................................................................ ..364 15.13 Stock market volatility ....................................................................... .. 367 Summary ................................ ...................................................... ..368 Further reading ................................................................................ .. 369 Questions and problems ..................................................................... .. 369 Assignment questions ........................................................................ .. 371 Appendix: Taylor series expansions and hedge parameters ...................... .. 373 Chapter 16 Volatility smiles ........................................... ..‘ ............................................. ..375 16.1 Put—call parity revisited ..................................................................... ..375 16.2 Foreign currency options .................................................................... .. 376 16.3 Equity options .................................................................................. ..379 16.4 The volatility term structure and volatility surfaces ................................ .. 381 16.5 Greek letters .................................................................................... .. 383 16.6 When a single large jump is anticipated ............................................... .. 383 Summary ............... ... ....................................................................... .. 385 Further reading ................................................................................ .. 386 Questions and problems ..................................................................... ..386 Assignment questions ........................................................................ .. 388 Appendix: Determining implied risk—neutral distributions from volatility smiles .............................................................................. ..389 Chapter 17 Basic numerical procedures ........................................................................... ..391 17.1 Binomial trees .................................................................................. .. 391 17.2 Using the binomial tree for options on indices, currencies, and futures contracts .......................................................................................... .. 398 17.3 Binomial model for a dividend—paying stock ......................................... ..401 xii Contents 17.4 Alternative procedures for constructing trees ........................................ .. 406 17.5 Time-dependent parameters ............................................................... .. 409 176 Monte Carlo simulation .................................................................... .. 410 17.7 Variance reduction procedures ............................................................ .. 417 17.8 Finite difference methods ................................................................... .. 419 Summary ........................................................................................ .. 430 Further reading ................................................................................ .. 430 Questions and problems .................................................................... .. 431 Assignment questions ........................................................................ .. 432 Chapter 18 Value at risk ............................................................................................. .. 435 18.1 The VaR measure ............................................................................ .. 435 18.2 Historical simulation ......................................................................... .. 438 18.3 Model~building approach .................................................................. .. 440 18.4 Linear model ................................................................................... .. 442 18.5 Quadratic model ..' ............................................................................ .. 446 718.6 Monte Carlo simulation .................................................................... .. 448 18.7 Comparison of approaches ................................................................ .. 449 18.8 Stress testing and back testing ............................................................ .. 450 18.9 Principal components analysis ............................................................ .. 450 Summary ........................................................................................ .. 454 Further reading ................................................................................ .. 454 Questions and problems ........................................... ....................... .. 455 Assignment questions ........................................................................ .. 456 Appendix: Cash—flow mapping ....... .................................................. .. 458 Chapter 19 Estimating volatilities and correlations ............................................................ .. 461 19.1 Estimating volatility .......................................................................... .. 461 19.2 The exponentially weighted moving average model ................................ .. 463 19.3 The GARCH (1,1) model ................................................................. .. 465 19.4 Choosing between the models ............................................................ .. 466 19.5 Maximum likelihood methods ............................................................ .. 467 19.6 Using GARCH (l, 1) to forecast future volatility .................................. .. 471 19.7 Correlations ..................................................................................... .. 475 Summary ........................................................................................ .. 477 Further reading ................................................................................ .. 478 Questions and problems .................................................................... .. 478 Assignment questions ........................................................................ .. 480 Chapter 20 Credit risk ................................................................................................ .. 481 20.1 Credit ratings ................................................................................... .. 481 20.2 Historical default probabilities ........................................................... .. 482 20.3 Recovery rates ................................................................................. .. 483 20.4 Estimating default probabilities from bond prices .................................. .. 484 20.5 Comparison of default probability estimates ......................................... .. 486 20.6 Using equity prices to estimate default probabilities .............................. .. 489 207 Credit risk in derivatives transactions .................................................. .. 491 20.8 Credit risk mitigation ...................................................... ................ .. 493 20.9 Default correlation ........................................................................... .. 495 20.10 Credit VaR ..................................................................................... .. 499 Summary ........................................................................................ .. 502 Further reading ................................................................................ .. 503 Questions and problems .................................................................... .. 503 Assignment questions ........................................................................ .. 505 Contents Chapter 21 Chapter 22 Chapter 23 Chapter 24 xiii Credit derivatives ........................................................................................ .. 507 21.1 Credit default swaps ...... .................................................................. .. 507 21.2 Credit indices ....................................................... ......................... .. 510 21.3 Valuation of credit default swaps .............................. .. ........................ .. 510 21.4 CDS forwards and options ................................................................. ..514 21.5 Total return swaps ............................................................................ .. 515 21.6 Basket credit default swaps .................................. ............................. .. 516 21.7 Collateralized debt obligations .............................. ............................ .. 516 21.8 Valuation of a basket CD8 and CD0 .................................................. ..519 21.9 Convertible bonds ............................................................................. .. 520 Summary ......................................................................................... .. 523 Further reading ................................................................................ .. 524 Questions and problems ..................................................................... .. 524 Assignment questions ........................................................................ .. 526 Exotic options ............................................................................................ ..529 22.1 Packages .......................................................................................... .. 529 22.2 Nonstandard American options ............................ .._ ............................ .. 530 22.3 Forward start options ........................................................................ .. 531 22.4 Compound options ........................................................................... .. 531 22.5 Chooser options ............................................................................... .. 532 22.6 Barrier options .......................................................... .1 ..................... .. 533 22.7 Binary options .................................................................................. .. 535 22.8 Lookback options ............................................................................. .. 536 22.9 Shout options ................................................................................... .. 537 22.10 Asian options ................................................................................... ..538 22.11 Options to exchange one asset for another ............................................ .. 540 22.12 Options involving several assets ........... .. .............................................. .. 541 22.13 Static options replication .................................................................... .. 541 Summary ................................ ... ...................................................... .. 544 Further reading ........................ ...................................................... .. 544 Questions and problems ..................................................................... .. 545 Assignment questions ........................................................................ .. 547 Appendix: Calculation of moments for valuation of basket options and Asian options .................................................................... ..549 Weather, energy, and insurance derivatives ....................................................... ..551 23.1 Review of pricing issues ..................................................................... .. 551 23.2 Weather derivatives ........................................................................... .. 552 23.3 Energy derivatives ........................................................................ 553 23.4 Insurance derivatives ......................................................................... .. 556 Summary ......................................................................................... .. 557 Further reading ................................................................................ .. 558 Questions and problems ..................................................................... .. 558 Assignment question .............................................................. ..L ........ .. 559 More on models and numerical procedures ....................................................... ..561 24.1 Alternatives to Black—Scholes ............................................................. .. 562 24.2 Stochastic volatility models ................................................................. .. 566 24.3 The IVF model ................................................................................ .. 568 24.4 Path—dependent derivatives ................................................................. .. 569 24.5 Barrier options .' ................................................................................ .. 573 24.6 Options on two correlated assets ......................................................... .. 576 24.7 Monte Carlo simulation and American options ..................................... ..579 Xiv Contents Summary ........................................................................................ .. 583 Further reading ................................................................................ .. 584 Questions and problems .................................................................... .. 585 Assignment questions ........................................................................ .. 586 Chapter 25 Martingales and measures ............................................................................ .. 589 25.1 The market price of risk .................................................................... .. 590 25.2 Several state variables ....................................................................... .. 593 25.3 Martingales ..................................................................................... .. 594 25.4 Alternative choices for the numeraire .................................................. .. 596 25.5 Extension to several factors ............................................................... .. 599 25.6 Applications .................................................................................... .. 600 25.7 Change of numeraire ........................................................................ .. 602 Summary ....................................... ............................................... .. 603 Further reading ................................................................................ .. 604 Questions and problems .................................................................... .. 604 ~ Assignment questions ........................................................................ .. 606 Appendix: Handling multiple sources of uncertainty .............................. .. 607 Chapter 26 Interest rate derivatives: the standard market models ......................................... .. 611 26.1 Black’s model .................................................................................. .. 611 26.2 Bond options ................................................................................... .. 614 26.3 Interest rate caps and floors ............................................................... .. 619 26.4 European swap options ............................................ ....................... .. 625 26.5 Generalizations ....................................................... ....................... .. 629 26.6 Hedging interest rate derivatives ..... .................................................. .. 630 ' Summary ........................................................................................ .. 630 Further reading ................................................................................ .. 631 Questions and problems .................................................................... .. 631 Assignment questions ........................................................................ .. 632 Chapter 27 Convexity, timing, and quanto adjustments ...................................................... .. 635 27.1 Convexity adjustments ....................................................................... .. 635 27.2 Timing adjustments .......................................................................... .. 639 27.3 Quantos .......................................................................................... .. 641 Summary ........................................................................................ .. 644 Further reading ................................................................................ .. 644 Questions and problems .................................................................... .. 645 Assignment questions ........................................................................ .. 646 Appendix: Proof of the convexity adjustment formula ........................... .. 648 Chapter 28 Interest rate derivatives: models of the short rate ............................................... .. 649 281 Background ..................................................................................... .. 649 28.2 Equilibrium models .......................................................................... .. 650 28.3 No—arbitrage models ......................................................................... .. 654 28.4 Options on bonds ............................................................................ .. 658 28.5 Volatility structures ........................................................................... .. 659 28.6 Interest rate trees ........................................................ .L .................... .. 660 28.7 A general tree-building procedure ....................................................... .. 662 28.8 Calibration .................................................................... ................ .. 672 28.9 Hedging using a one-factor model ...................................................... .. 673 Summary ........................................................................................ .. 673 Further reading ................................................................................ .. 674 Questions and problems .................................................................... .. 674 Assignment questions ........................................................................ .. 676 Contents xv Chapter 29 Interest rate derivatives: HJM and LMM ....................................................... ..679 29.1 The Heath, Jarrow, and Morton model ................................................ .. 679 29.2 The LIBOR market model ................................... .......................... .. 682 29.3 Mortgage—backed securities ................................................................. .. 692 Summary ......................................................................................... ..694 Further reading ................................................................................ .. 695 Questions and problems ..................................... ..r .............................. ..696 Assignment questions ........................................ ..'. ............................. .. 696 Chapter 30 Swaps Revisited .......................................................................................... ..697 30.1 Variations on the vanilla deal ............................................................. ..697 30.2 Compounding swaps ......................................................................... .. 699 30.3 Currency swaps ................................................................................ .. 700 30.4 More complex swaps ......................................................................... .. 701 30.5 Equity swaps .................................................................................... .. 704 30.6 Swaps with embedded options ............................................................ .. 705 30.7 Other swaps ..................................................................................... .. 708 Summary ......................................................................................... ..709 Further reading ................................................................................ .. 710 Questions and problems ..................................................................... .. 710 . Assignment questions ........................................................................ .. 711 Chapter 31 Real options ...................................................................... ....................... ..713 31.1 Capital investment appraisal ............................................................... .. 713 31.2 Extension of the risk~neutral valuation framework ................................. .. 714 31.3 Estimating the market price of risk ...................................................... .. 716 31.4 Application to the valuation of a business ............................................ .. 717 31.5 Commodity prices ............................................................................. .. 717 31.6 Evaluating options in an investment opportunity ................................... .. 722 Summary ......................................................................................... ..727 Further reading ................................................................................ .. 727 Questions and problems ............ ....................................................... .. 727 Assignment questions ........................................................................ .. 728 Chapter 32 Derivatives mishaps and what we can learn from them ....................................... ..729 32.1 Lessons for all users of derivatives ....................................................... .. 729 32.2 Lessons for financial institutions ......................................................... .. 733 32.3 Lessons for nonfinancial corporations .................................................. ..737 Summary ......................................................................................... .. 738 Further reading ................................................................................ .. 738 Glossary of terms ......................................................................................................... ..741 DerivaGem software ..................................................................................................... ..761 Major exchanges trading futures and options ..................................................................... ..767 Table for N(x) when x g 0 ................... .; ........................................................................ ..768 Table for N(x) when x 2 0 ............................................................................................. ..769 Author index ............................................................................................................... ..771 Subject index ............................................................................................................... .. 775 BUSINESS SNAPSHOTS a oppwwwssaaawwwweewwwwrr lQP"‘leHlQHMIQr-‘kalvt—‘luh-‘IUMlQHle—I ,_.. 13.1 [\J l\J l\) Ix) 10 |\) lx) l\J lQ 503999”??? ..‘y—qu—wm—r L» p ..l UJUJ 00 \J L» J 30. 31.1 32.1 32.2 Hedge Funds ........................................... ................................................ ..9 The Barings Bank Disaster ......................................................................... .. 15 The Unanticipated Delivery of a Futures Contract .......................................... .22 Long—Term Capital Management’s Big Loss ................................................. .. 30 Hedging by Gold Mining Companies ........................................................... .. 52 Metallgesellschaft: Hedging Gone Awry ....................................................... .. 68 What isthe Risk-Free Rate? ....................................................................... .. 77 Orange County’s Yield Curve Plays ............................................................. .. 86 Kidder Peabody’s Embarrassing Mistake .................................................... .. 103 A Systems Error? .................................... ..‘ .............................................. .. 109 The CME Nikkei 225 Futures Contract ...................................................... .. 111 Index Arbitrage in October 1987 ............................................................... .. 112 Day Counts Can Be Deceptive .................................................................. .. 130 The Wild Card Play ................................................................................ .. 136 Asset-Liability Management by Banks ...................................................... .. 144 Extract from Hypothetical Swap Confirmation ............................................ .. 156 The Hammersmith and Fulham Story ........................................................ .. 173 Gucci Group’s Large Dividend ................................................................. .. 189 Tax Planning Using Options .................................................................... .. 198 Executive Stock Options ................................................. .., ...................... .. 199 Put—Call Parity and Capital Structure ....................................................... .. 214 1.03ng Money with Box Spreads ............................................................... .. 230 How to Make Money from Trading Straddles ............................................. .. 235 Mutual Fund Returns Can Be Misleading .................................................. .. 285 What Causes Volatility? ........................................................................... .. 289 Warrants, Executive Stock Options, and Dilution ........................................ .. 299 Can We Guarantee that Stocks Will Beat Bonds in the Long Run? ................ .. 319 Dynamic Hedging in Practice ................................................................... .. 363 Was Portfolio Insurance to Blame for the Crash of 1987? ............................. .. 367 Making Money from Foreign Currency Options .......................................... .. 379 Crashophobia .................................................................... ................... .. 381 Calculating Pi with Monte Carlo Simulation ............................................... .. 410 Checking BIack—Scholes .......................................................................... .. 413 How Bank Regulators Use VaR ................................................................ .. 436 Downgrade Triggers and Enron’s Bankruptcy ............................................. .. 496 Basel II ................................................................................................. .. 501 Who Bears the Credit Risk? ..................................................................... .. 508 Is the CDS Market 21 Fair Game? ............................................................. .. 514 Correlation Smiles ................................................................................... .. 520 Is Delta Hedging Easier or More Difficult for Exotics? ................................. .. 542 Put—Call Parity for Caps and Floors ......................................................... .. 621 Swaptions and Bond Options ................................................................... .. 626 Siegel’s Paradox ...................................................................................... .. 643 10s and POs .......................................................................................... .. 693 Hypothetical Confirmation for Nonstandard Swap ...................................... .. 698 Hypothetical Confirmation for Compounding Swap .................... ............... .. 699 Hypothetical Confirmation for Equity Swap ............................................... .. 705 Procter and Gamble’s Bizarre Deal ............................................................ .. 709 Valuing Amazoncorn .............................................................................. .. 718 Big Losses by Financial Institutions ........................................................... .. 730 Big Losses by Nonfinancial Companies ...................................................... .. 731 TECHNICAL NOTES E‘P‘P‘PJPT“ 00>! ll. 1’) 13. 14. 15. 16. 17. 18. 19. 20 Available on the Author’s 'Website www.rotman.utoronto.ca/~hull Convexity Adjustments to Eurodollar Futures Properties of the. Lognorrnal Distribution Warrant Valuation When Value of Equity plus Warrants Is Lognormal Exact Procedure for Valuing American Calls on Stocks Paying a Single Dividend Calculation of the Cumulative Probability in a Bivariate Normal Distribution Differential Equation for Price of a Derivative on a Stock Paying a Known Dividend Yield , Differential Equation for Price of a Derivative on a Futures Price . Analytic Approximation for Valuing American Options Generalized Tree-Building Procedure The Cornish—Fisher Expansion to Estimate VaR Manipulation of Credit Transition Matrices Calculation of Cumulative Noncentral Chi-Square Distribution Efficient Procedure for Valuing American—Style Lookback Options The Hull—White Two~Factor Model Valuing Options on Coupon—Bearing Bonds in a One—Factor Interest Rate Model Construction of an Interest Rate Tree with Nonconstant Time Steps and Non— constant Parameters The Process for the Short Rate in an H] M Term Structure Model Valuation of a Compounding Swap Valuation of an Equity Swap . A Generalization of the Risk—Neutral Valuation Result Preface It is sometimes hard for me to believe that the first edition of this book was only 330 pages and 13 chapters long! Over the last 15 years I have had to expand and adapt the book to keep up with the fast pace of change in derivatives markets. Like earlier editions, the book serves several markets. It is appropriate for graduate courses in business, economics, and financial engineering. It can be used on advanced undergraduate courses when students have good quantitative skills. Many practitioners involved in derivatives markets find the book useful. I am pleased that half the purchasers of the book have historically been analysts, traders, and other market practitioners. ' , One of the key decisions that must be made by an author who is writing in the area of derivatives concerns the use of mathematics. If the level of mathematical sophistication is too high, the material is likely to be inaccessible to many students and practitioners. If it is too low, some important issues will inevitably be treated in a rather superficial way. I have tried to be particularly careful about the way I use both mathematics and notation in the book. Nonessential mathematical material has been either eliminated or included in end-of-chapter appendices and in the technical notes on my website. Concepts that are likely to be new to many readers have been explained carefully, and many numerical examples have been included. The book provides a comprehensive treatment Of derivatives and risk management. It assumes that the reader has taken introductory courses in finance and in probability and statistics. No prior knowledge of options, futures contracts, swaps, or other derivative instruments is assumed. It is not therefore necessary for students to take an elective course in investments prior to taking a course based on this book. There are many different ways Options, Futures, and Other Derivatives can be used in the classroom. Instructors teaching a first course in derivatives may wish to spend most time on the first half of the book; those teaching more advanced courses will find that many different combinations of chapters in the second half of the book can be used. 1 find the material in Chapter 32 works well at the end of either an introductory or an advanced course. ‘ What’s New? Material has been updated and improved throughout the book. The changes in this edition include: 1. Complete rewrites of the chapters on credit risk and credit derivatives (Chapters 20 and 21) to reflect market developments in these important areas. The rewrites result in chapters that are up to date and easier to teach from than the corresponding chapters in the fifth edition. xix XX 10. 11. 12. Preface . The opening six chapters have been replaced by seven chapters that cover forward, futures, and swap contracts in a more student—friendly way. The chapter on hedging has been moved to Chapter 3. Chapter 4 is now devoted to understanding how interest rates are calculated and used. Chapter 5 covers the determination of futures and forward prices. Chapter 6 deals with interest rate futures, and Chapter 7 covers swaps. . Over 50 highlighted descriptions of real-world situations and interesting issues, referred to as Business Snaps/tots, illustrate points being made in the text. There is more discussion of how models can be implemented with Excel (see, for example, Monte Carlo simulation in Chapter 17, GARCH models in Chapter 19, and the variance—gamma model in Chapter 24). Excel Spreadsheets illustrating model implementations are available from my website. . A series of Technical Notes are available from my website. This means that less purely technical material needs to be included in the book. As a result, the presentation is streamlined and more student friendly. . DerivaGem Version 1.51 is included. One-change from the previous version of DerivaGem is that spreadsheets are now unlocked in the Calculator. . The binomial tree chapter (Chapter 11) and the swaps chapter (Chapter 7) have been extended so that there is a more complete coverage of these topics at one place in the book. . There is a new chapter on “Convexity, Timing, and Quanto Adjustments”. Previously the material in this chapter was included in the chapters on “Martin- gales and Measures” and “Interest Rate Derivatives: The Standard Market Models”. . Sequencing of chapters in the second half of the book has been changed to better meet the needs of students and instructors. Many new topics are included. For example, I cover the size of derivatives markets in Chapter 1, Basel II in Chapter 20, and the variance—gamma model in Chapter 24. Other topics are discussed in more depth than in the fifth edition. For example, there is more on convexity adjustments to Eurodollar futures (Chapter 5), copula models (Chapters 20 and 21), and executive stock options (Chapters 8 and 13). One change has been made to the mathematical notation. 5t, 5x, etc., have been replaced by At, Ax, etc. (This reverses a change in the previous edition where I was trying to avoid overworking A—-but found that the change was not popular!) New end-of—chapter problems have been added. The whole book (including end-of~chapter references) has been fully updated and many -' changes have been made to improve the presentation of material. Software Version 1.51 of DerivaGem is included with this book. This consists of two Excel applications: the Options Calculator and the Applications Builder. The Options Calculator consists of easy-to~use software for valuing a wide range of options. The worksheets are now unlocked. The Applications Builder consists of a number of Excel functions from which users can build their own applications. It includes a number of sample applications and enables students to explore the properties of options and Preface xxi numerical procedures more easily: It also allows more interesting assignments to be designed. w The software is described more fully at the end of the book."Updates to the software -can be downloaded from my website ' WWW.rotman.utoronto.ca/~hull Slides Several hundred PowerPoint slides can be downloaded from my website. Instructors who adopt the text are welcome to adapt the slides to meet their own needs. Solutions Manual As in the fifth edition, end-of-chapter problems are divided into two groups: “Questions and Problems” and “Assignment Questions”. Solutions to the Questions and Problems are in OpIions, Futures, and Other Derivatives: Solutions M ant/o] (ISBN: 0—13—149906—8), which is published by Prentice Hall and can be purchased by students. Technical Notes A new feature of the sixth edition is the use of Technical Notes. These elaborate on points made in the text and can be downloaded from my website. WWW.rotman.utoronto.ca/ ~hu11 By not including the Technical Notes in the book, I was able to streamline the presentation of material so that it is more student friendly. Online Training In conjunction with Learning Dividends,lnc., I have developed e—Learning material entitled Hull on Derivatives to accompany the first half of the book. This consists of 14 modules with fully animated and narrated instruction. For more information visit WWW.hu]londerivatives.com Acknowledgments Many people have played a part in the production of this book. Academics, students, and practitioners who have made excellent and useful suggestions include Farhang Aslani, Jas Badyal, Emilio Barone, Giovanni Barone-Adesi, Alex Bergier, George Blazenko, Laurence Booth, Phelim Boyle, Peter Carr, Don Chance, J.—P. Chateau, Ren-Raw Chen, Dan Cline, George Constantinides, Michel Crouhy, Emanuel Derman, Brian Donaldson, Dieter Dorp, Scott Drabin, Jerome Duncan, Steinar Ekern, David Forfar, David Fowler, Louis Gagnon, Richard Goldfarb, Dajiang Guo, Jorgen Hallbeck, Ian Hawkins, Michael Hemler, Steve Heston, Bernie Hildebrandt, Michelle Hull, Andrew Karolyi, Kiyoshi Kato, Kevin Kneafsy, Iain MacDonald, Bill Margrabe, Eddie Mizzi, Izzy Nelkin, Neil Pearson, Paul Potvin, Shailendra Pandit, Eric Reiner, Richard Rendleman, Gordon Roberts, Chris Robinson, Cheryl Rosen, John Rumsey, Ani Sanyal, Klaus Schurger, Eduardo Schwartz, Michael Selby, Piet Sercu, Duane Stock, Edward Thorpe, Yisong Tian, Alan Tucker, P. V. Viswanath, George Wang, Jason Wei, Bob Whaley, Alan White, Hailiang Yang, Victor Zak, and Jozef Zemek. xxii Preface I am particularly grateful to Eduardo Schwartz, who read the original manuscript for the first edition and made many comments that led to significant improvements, and to Richard Rendleman and George Constantinides, who made specific suggestions that led to improvements in more recent editions. The first five editions of this book were very popular with practitioners and their comments and suggestions have led to many improvements in the book. I would particularly like to thank Dan Cline and David Forfar. The students in my elective courses on derivatives at the University of Toronto have also played a significant role the evolution of the book. Yves Noth from the University of St. Gallen provided excellent research assistance for this edition. Alan White, a colleague at the University of Toronto, deserves a special acknowledg- ment. Alan and I have been carrying out joint research in the area of derivatives for the last 22 years. During that time we have spent countless hours discussing different issues concerning derivatives. Many of the new ideas in this book, and many of the new ways used to explain old ideas, are as much Alan’s as mine. Alan read the original version of this book very carefully and made many excellent suggestions for improvement. He has also done most of the development work on the DerivaGem software. Special thanks are due to many people at Prentice Hall for their enthusiasm, advice, and encouragement. I would particularly like to thank David Alexander, my editor, and Francesca Calogero, the finance assistant editor. I am also grateful to Scott Barr, Leah Jewell, Paul Donnelly, and Maureen Riopelle, who at different times have played key roles in the development of the book. I welcome comments on the book from readers. My email address is: hull©rotman.ut oronto . ca John Hull Joseph L. Rotman School of Management University of Toronto ...
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0_Contents - CONTENTS IN BRIEF List of Business Snapshots

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