SEVENTH EDITION FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS GLOBAL EDITION John C. Hull / Maple Financial Group Professor of Derivatives and Risk Management Joseph L. Rotman School of Management University of Toronto Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
CONTENTS IN BRIEF Business snapshots xv Preface xvii 1. Introduction 1 2. Mechanics of futures markets 21 3. Hedging strategies using futures /. 47 4. Interest rates 79 5. Determination of forward and futures prices 103 6. Interest rate futures 131 7. Swaps 157 8. Securitization and the credit crisis of 2007 189 9. Mechanics of options markets 205 10. Properties of stock options." 227 11. Trading strategies involving options 249 12. Introduction to binomial trees 267 13. Valuing stock options: The Black-Scholes-Merton model 289 14. Derivatives markets in developing countries 317 15. Options on stock indices and currencies 323 16. Futures options 339 17. The Greek letters 355 18. Binomial trees in practice 387 19. Volatility smiles ( 409 20. Value at risk 425 21. Interest rate options 457 22. Exotic options and other nonstandard products 477 23. Credit derivatives 497 24. Weather, energy, and insurance derivatives 517 25. Derivatives mishaps and what we can learn from them 525 Answers to quiz questions 537 Glossary of terms 561 DerivaGem software 579 Major exchanges trading futures and options 585 Tables for N(x) 586 Index 589
Contents Business Snapshots Preface Chapter 1: Introduction 1 1.1 Futures Contracts 1 1.2 History of Futures Markets 2 1.3 The Over-the-Counter Market 4 1.4 Forward Contracts 5 1.5 Options 6 1.6 History of Options Markets 8 1.7 Types of Traders!. 9 1.8 Hedgers 9 1.9 Speculators 12 1.10 Arbitrageurs 15 1.11 Dangers 16 Summary 16 Further Reading 18 Quiz 18 Practice Questions 18 Further Questions 19 Chapter 2: Mechanics of Futures Markets 21 2.1 Opening and Closing Futures Positions 21 2.2 Specification of a Futures Contract 22 2.3 Convergence of Futures Price to Spot Price 25 2.4 The Operation of Margins 26 2.5 OTC Markets 29 2.6 Newspaper Quotes 31 2.7 Delivery 34 2.8 Types of Trader and Types of Order 35 2.9 Regulation 36 2.10 Accounting and Tax 38 2.11 Forward vs. Futures Contracts 40 Summary 42 Further Reading 43 Quiz 43 Practice Questions 43 Further Questions 44 xv xvii vii
Vlll Contents Chapter 3: 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 57 3.5 Stock Index Futures 61 3.6 Rolling the Hedge Forward 67 Summary 68 Further Reading.^ 69 Quiz ".'...:.'.: 70 Practice Questions 71 Further Questions 72 Appendix: Review of Key Concepts in Statistics and the CAPM 74 Chapter 4: Interest Rates 79 4.1 Types of Rates 79 4.2 Measuring Interest Rates 81 4.3 Zero Rates 83 4.4 Bond Pricing 84 4.5 Determining Treasury Zero Rates 86 4.6 Forward Rates 88 4.7 Forward Rate Agreements 90 4.8 Theories of the Term Structure of Interest Rates '. 93 Summary 95 Further Reading 96 Quiz 96 Practice Questions 97 Further Questions 98 Appendix: Exponential and Logarithmic Functions 100 Chapter 5: Determination of Forward and Futures Prices 103 5.1 Investment Assets vs. Consumption Assets 103 5.2 Short Selling 104 5.3 Assumptions and Notation 105 5.4 Forward Price for an Investment Asset 106 5.5 Known Income 109 5.6 Known Yield Ill 5.7 Valuing Forward Contracts Ill 5.8 Are Forward Prices and Futures Prices Equal? 114 5.9 Futures Prices of Stock Indices 114 5.10 Forward and Futures Contracts on Currencies 116 5.11 Futures on Commodities 120 5.12 The Cost of Carry ^.. 123 5.13 Delivery Options 123 5.14 Futures Prices and the Expected Spot Prices 124 Summary 126 Further Reading 127 Quiz 128
Contents ix Practice Questions 128 Further Questions 130 Chapter 6: Interest Rate Futures 131 6.1 Day Count and Quotation Conventions 131 6.3 Treasury Bond Futures 134 6.4 Eurodollar Futures 139 6.5 Duration 142 6.6 Duration-Based Hedging Strategies Using Futures 147 Summary 151 Further Reading 152 Quiz 152 Practice Questions 153 Further Questions 154 Chapter 7: Swaps 157 7.1 Mechanics of Interest Rate Swaps 157 7.2 Day Count Issues 164 7.3 Confirmations ". 164 7.4 The Comparative-Advantage Argument.7. 165 7.5 The Nature of Swap Rates." 168 7.6 Determining LIBOR/Swap Zero Rates >..169 7.7 Valuation of Interest Rate Swaps 170 7.8 Currency Swaps 175 7.9 Valuation of Currency Swaps 178 7.10 Credit Risk 180 7.11 Other Types of Swap 182 Summary 184 Further Reading 185 Quiz 185 Practice Questions 186 Further Questions 188 Chapter 8: Securitization and the Credit Crisis of 2007 189 8.1 Securitization 189 8.2 The U.S. Housing Market 193 8.3 What Went Wrong? 197 8.4 Avoiding Future Crises 198 Summary 201 Further Reading 202 Quiz 202 Practice Questions 203 _ Further Questions 203 Chapter 9: Mechanics of Options Markets 205 9.1 Types of Option 205 9.2 Option Positions 208 9.3 Underlying Assets 210 9.4 Specification of Stock Options 211 9.5 Trading 215 9.6 Commissions 216
X Contents 9.7 Margins 217 9.8 The Options Clearing Corporation 218 9.9 Regulation 219 9.10 Taxation 219 9.11 Warrants, Employee Stock Options, and Convertibles 221 9.12 Over-the-Counter Markets 222 Summary 222 Further Reading 223 Quiz ; 223 Practice Questions "!...:.r..~. 224 Further Questions 225 Chapter 10: Properties of Stock Options 227 10.1 Factors Affecting Option Prices 227 10.2 Assumptions and Notation : 231 10.3 Upper and Lower Bounds for Option Prices 231 10.4 Put-Call Parity 235 10.5 Calls on a Non-Dividend-Paying Stock 239 10.6 Puts on a Non-Dividend-Paying Stock 240 10.7 Effect of Dividends : 243 Summary 244 Further Reading 245 Quiz 245 Practice Questions 246 Further Questions 247 Chapter 11: Trading Strategies Involving Options 249 11.1 Strategies Involving a Single Option and a Stock 249 11.2 Spreads 251 11.3 Combinations 260 11.4 Other Payoffs 263 Summary 263 Further Reading 264 Quiz 264 Practice Questions 264 Further Questions 265 Chapter 12: Introduction to Binomial Trees 267 12.1 A One-Step Binomial Model and a No-Arbitrage Argument 267 12.2 Risk-Neutral Valuation... 271 12.3 Two-Step Binomial Trees 273 12.4 A Put Example 276 12.5 American Options 277 12.6 Delta 278 12.7 Determining u and d 279 12.8 Increasing the Number of Time Steps 280 12.9 Options on Other Assets 281 Summary 286 Further Reading 286 Quiz 286
Contents xi Practice Questions 287 Further Questions 288 Chapter 13: Valuing Stock Options: The Black-Scholes-Merton Model 289 13.1 Assumptions about How Stock Prices Evolve 290 13.2 Expected Return 293 13.3 Volatility 293 13.4 Estimating Volatility from Historical Data 295 13.5 Assumptions Underlying Black-Scholes-Merton 298 13.6 The Key No-Arbitrage Argument 298 13.7 The Black-Scholes-Merton Pricing "Formulas 299 13.8 Risk-Neutral Valuation 302 13.9 Implied Volatilities 7 303 13.10 Dividends 304 13.11 Valuing Employee Stock Options 306 Summary 310 Further Reading 311 Quiz 311 Practice Questions 312 Further Questions.' 313 Appendix: The Early Exercise of American Call Options on Dividend-Paying Stocks 315 Chapter 14: Derivatives Markets in Developing Countries 317 14.1 China's Markets 317 14.2 India's Markets 319 14.3 Other Developing Countries 320 Summary 320 Further Reading 321 Chapter 15: Options on Stock Indices and Currencies 323 15.1 Options on Stock Indices 323 15.2 Currency Options 326 15.3 Options on Stocks Paying Known Dividend Yields 328 15.4 Valuation of European Stock Index Options 330 15.5 Valuation of European Currency Options 332 15.6 American Options 334 Summary 335 Further Reading 335 Quiz...: 336 Practice Questions 336 Further Questions 338 Chapter 16: Futures Options 339 16.1 Nature of Futures Options 339 16.2 Reasons for the Popularity of Futures Options 341 16.3 European Spot and Futures Options 342 16.4 Put-Call Parity 342 16.5 Bounds for Futures Options 344 16.6 Valuation of Futures Options Using Binomial Trees 344 16.7 A Futures Price as an Asset Providing a Yield 347
xii Contents 16.8 Black's Model for Valuing Futures Options 347 16.9 Using Black's Model Instead of Black-Scholes-Merton 347 16.10 American Futures Options vs. American Spot Options 349 16.11 Futures-Style Options 349 Summary 350 Further Reading 351 Quiz 351 Practice Questions 351 Further Questions... 353 Chapter 17: The Greek Letters...!...:... 355 17.1 Illustration 355 17.2 Naked and Covered Positions 356 17.3 A Stop-Loss Strategy 356 17.4 Delta Hedging -. 358 17.5 Theta 365 17.6 Gamma 367 17.7 Relationship Between Delta, Theta, and Gamma 370 17.8 Vega 371 17.9 Rho 7. 373 17.10 The Realities of Hedging 374 17.11 Scenario Analysis 374 17.12 Extensions of Formulas 376 17.13 Creating Options Synthetically for Portfolio Insurance 378 17.14 Stock Market Volatility 380 Summary 381 Further Reading 382 Quiz 382 Practice Questions 383 Further Questions 385 Chapter 18: Binomial Trees in Practice 387 18.1 The Binomial Model for a Non-Dividend-Paying Stock 387 18.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts 394 18.3 The Binomial Model for a Dividend-Paying Stock 397 18.4 Extensions of the Basic Tree Approach 399 18.5 Alternative Procedure for Constructing Trees 401 18.6 Monte Carlo Simulation... 404 Summary : 405 Further Reading 406 Quiz 406 Practice Questions 406 Further Questions 407 Chapter 19: Volatility Smiles 409 19.1 Foreign Currency Options 409 19.2 Equity Options 412 19.3 The Volatility Term Structure and Volatility Surfaces 414 19.4 When a Single Large Jump Is Anticipated 416
Contents xiii Summary 417 Further Reading 418 Quiz 419 Practice Questions 419 Further Questions 420 Appendix: Why the Put Volatility Smile is the Same as the Call Volatility Smile 422 Chapter 20: Value at Risk 425 20.1 The VaR Measure 425 20.2 Historical Simulation \...:..;.....428 20.3 Model-Building Approach 432 20.4 Generalization of Linear Model 435 20.5 Quadratic Model 439 20.6 Estimating Volatilities and Correlations 442 20.7 Comparison of Approaches 448 20.8 Stress Testing and Back Testing : 449 Summary 449 Further Reading 450 Quiz : 451 Practice Questions 452 Further Questions 453 Appendix: Cash-Flow Mapping 455 Chapter 21: Interest Rate Options 457 21.-1 Exchange-Traded Interest Rate Options 457 21.2 Embedded Bond Options 459 21.3 Black's Model 459 21.4 European Bond Options 461 21.5 Interest Rate Caps 463 21.6 European Swap Options 469 21.7 Term Structure Models 472 Summary 473 Further Reading 474 Quiz 1 474 Practice Questions 475 Further Questions 476 Chapter 22: Exotic Options and Other Nonstandard Products 477 22.1 Exotic Options.477 22.2 Agency Mortgage-Backed Securities 483 22.3 Nonstandard Swaps 485 Summary 492 Further Reading 492 Quiz 493 Practice Questions 493 Further Questions 494 Chapter 23: Credit Derivatives 497 23.1 Credit Default Swaps 497 23.2 Determining CDS Spreads 502
xiv Contents 23.3 Total Return Swaps 507 23.4 CDS Forwards and Options 509 23.5 Collateralized Debt Obligations 509 Summary 513 Further Reading 513 Quiz 514 Practice Questions 514 Further Questions 515 Chapter 24: Weather, Energy, and Insurance Derivatives 517 24.1 Weather Derivatives..';...;.. 517 24.2 Energy Derivatives 518 24.3 Insurance Derivatives : 521 Summary 522 Further Reading 523 Quiz : 523 Practice Questions 524 Further Question 524 Chapter 25: Derivatives Mishaps and What We Can Learn From Them 525 25.1 Lessons for All Users of Derivatives 525 25.2 Lessons for Financial Institutions 529 25.3 Lessons for Nonfinancial Corporations 534 Summary 535 Further Reading 536 Answers to Quiz Questions 537 Glossary of Terms 561 DerivaGem Software 579 The Options Calculator 580 The Applications Builder 583 Major Exchanges Trading Futures and Options 585 Table for N(x) When x < 0 586 Table for N(x) When x > 0 587 Index \ 589