NINTH EDITION FUNDAMENTALS OF FUTURES AND OPTIONS MARKETS John C. Hüll Maple Financial Group Professor of Derivatives and Risk Management Joseph L. Rotman School of Management University of Toronto PEARSON Boston Columbus Indianapolis New York San Francisco Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Säo Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo
Contents Preface xv 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 6 1.5 Options 7 1.6 History of Options Markets 10 1.7 Types of Trader 11 1.8 Hedgers 11 1.9 Speculators 14 1.10 Arbitrageurs 17 1.11 Dangers 18 18 20 20 20 22 Chapter 2: Futures Markets and Central Counterparties 24 2.1 Opening and Closing Futures Positions 24 2.2 Specification of a Futures Contract 25 2.3 Convergence of Futures Price to Spot Price 28 2.4 The Operation of Margin Accounts 29 2.5 OTC Markets 32 2.6 Market Quotes 35 2.7 Delivery 37 2.8 Types of Trader and Types of Order 38 2.9 Regulation 39 2.10 Accounting and Tax 40 2.11 Forward vs. Futures Contracts 42 44 45 45 46 47 vii
Contents Chapter 3: Hedging Strategie* Using Futures 49 3.1 Basic Principles 49 3.2 Arguments for and Against Hedging 52 3.3 Basis Risk 55 3.4 Gross Hedging 59 3.5 Stock Index Futures 63 3.6 Stack and Roll 69 70 72 72 73 74 Appendix: Review of Key Concepts in Statistics and the CAPM 76 Chapter 4: Interest Rates 81 4.1 Types of Rates 81 4.2 Swap Rates 83 4.3 The Risk-Free Rate 84 4.4 Measuring Interest Rates 85 4.5 Zero Rates 87 4.6 Bond Pricing 88 4.7 Determining Zero Rates 89 4.8 Forward Rates 93 4.9 Forward Rate Agreements 95 4.10 Theories of the Term Structure of Interest Rates 97 100 101 101 102 103 Appendix: Exponential and Logarithmic Functions 105 Chapter 5: Determination of Forward and Futures Prices 107 5.1 Investment Assets vs. Consumption Assets 107 5.2 Short Selling 108 5.3 Assumptions and Notation 109 5.4 Forward Price for an Investment Asset 110 5.5 Known Income 113 5.6 Known Yield 115 5.7 Valuing Forward Contracts 115 5.8 Are Forward Prices and Futures Prices Equal? 118 5.9 Futures Prices of Stock Indices 118 5.10 Forward and Futures Contracts on Currencies 121 5.11 Futures on Commodities 124 5.12 The Cost of Carry 127 5.13 Delivery Options 127 5.14 Futures Prices and Expected Spot Prices 128 130 131
ix Interest Rate Futures Day Count and Quotation Conventions Treasury Bond Futures Eurodollar Futures Duration Duration-Based Hedging Strategies Using Futures Swaps Mechanics of Interest Rate Swaps Day Count Issues Confirmations The Comparative-Advantage Argument Valuation of Interest Rate Swaps How the Value Changes through Time Fixed-for-Fixed Currency Swaps Valuation of Fixed-for-Fixed Currency Swaps Other Currency Swaps Credit Risk Credit Default Swaps Other Types of Swaps Securitization and the Credit Crisis of 2007 Securitization The U.S. Housing Market What Went Wrong? The Aftermath Mechanics of Options Markets Types of Option Option Positions Underlying Assets Specification of Stock Options.132.132.134.136.136.139.143.148.152.156.157.157.158.159.161,162 167 167.168 171.174 175.178.180.181.182.183 184.185 185 186.188,190 190 194 198 200 202.202 203 203 204,205 205 208 210 211
x Contents 9.5 Trading 215 9.6 Commissions 216 9.7 Margin Requirements 217 9.8 The Options Clearing Corporation 219 9.9 Regulation 220 9.10 Taxation 220 9.11 Warrants, Employee Stock Options, and Convertibles 221 9.12 Over-the-Counter Options Markets 222 223 223 224 224 225 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 232 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 241 10.7 Effect of Dividends 243 244 245 245 246 247 Chapter 11: Trading Strategies Involving Options 249 11.1 Principal-Protected Notes 249 11.2 Strategies Involving a Single Option and a Stock 251 11.3 Spreads 253 11.4 Combinations 261 11.5 Other Payoffs 264 264 265 265 266 266 Chapter 12: Introduction to Binomial Trees 268 12.1 A One-Step Binomial Model and a No-Arbitrage Argument 268 12.2 Risk-Neutral Valuation 272 12.3 Two-Step Binomial Trees 274 12.4 A Put Example 277 12.5 American Options 278 12.6 Delta 279 12.7 Determining u and d 280 12.8 Increasing the Number of Time Steps 281 12.9 Using DerivaGem 282
xi Options on Other Assets Appendix: Derivation of the Black Scholes- -Merton Option Pricing Formula from Binomial Tree Valuing Stock Options: The Black-Scholes-Merton Model Assumptions about How Stock Prices Evolve Expected Return Volatility Estimating Volatility from Historical Data Assumptions Underlying Black-Scholes-Merton The Key No-Arbitrage Argument The Black-Scholes-Merton Pricing Formulas Risk-Neutral Valuation Implied Volatilities Dividends Appendix: The Early Exercise of American Call Options on Dividend-Paying Stocks Employee Stock Options Contractual Arrangements Do Options Align the Interests of Shareholders and Managers? Accounting Issues Valuation Backdating Scandals Options on Stock Indices and Currencies Options on Stock Indices Currency Options Options on Stocks Paying Known Dividend Yields Valuation of European Stock Index Options Valuation of European Currency Options American Options.282.287.287.287.288.289.291.293.294.297.298 299.301.302.304.306.307.309.311.312.313.313.315.316.318.318.320.321.323.324.325.326.326.327,327,328,328 331 333 335 338 339 340 341 341
xjj Contents 341 343 Chapter 16: Futures Options and Black s Model 344 16.1 Nature of Futures Options 344 16.2 Reasons for the Popularity of Futures Options 346 16.3 European Spot and Futures Options 347 16.4 Put-Call Parity 347 16.5 Bounds for Futures Options 349 16.6 A Futures Price as an Asset Providing a Yield 349 16.7 Black's Model for Valuing Futures Options 350 16.8 Using Black's Model Instead of Black-Scholes-Merton 350 16.9 Valuation of Futures Options Using Binomial Trees 351 16.10 American Futures Options vs. American Spot Options 354 16.11 Futures-Style Options 354 355 356 356 356 357 Chapter 17: The Greek Letters 359 17.1 Illustration 359 17.2 Naked and Covered Positions 360 17.3 Greek Letter Calculation 362 17.4 Delta 363 17.5 Theta 369 17.6 Gamma 371 17.7 Relationship Between Delta, Theta, and Gamma 374 17.8 Vega 378 17.9 Rho 377 17.10 The Realities of Hedging 379 17.11 Scenario Analysis 379 17.12 Extension of Formulas 380 17.13 Creating Options Synthetically for Portfolio Insurance 382 17.14 Stock Market Volatility 385 385 387 387 388 389 Chapter 18: Binomial Trees in Practice 391 18.1 The Binomial Model for a Non-Dividend-Paying Stock 391 18.2 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts 398 18.3 The Binomial Model for a Dividend-Paying Stock 401 18.4 Extensions of the Basic Tree Approach 405 18.5 Alternative Procedure for Constructing Trees 407 18.6 Monte Carlo Simulation 407
Contents xiii 409 410 410 411 412 Chapter 19: Volatility Smiles 413 19.1 Foreign Currency Options 413 19.2 Equity Options 416 19.3 The Volatility Term Structure and Volatility Surfaces 418 19.4 When a Single Large Jump Is Anticipated 420 421 422 423 423 424 Appendix: Why the Put Volatility Smile is the Same as the Call Volatility Smile 426 Chapter 20: Value at Risk and Expected Shortfall 428 20.1 The VaR and ES Measures 428 20.2 Historical Simulation 431 20.3 Model-Building Approach 436 20.4 Generalization of Linear Model 439 20.5 Quadratic Model 444 20.6 Estimating Volatilities and Correlations 446 20.7 Comparison of Approaches 451 20.8 Back Testing 452 452 453 453 454 455 Chapter 21: Interest Rate Options 458 21.1 Exchange-Traded Interest Rate Options 458 21.2 Embedded Bond Options 460 21.3 Black's Model 460 21.4 European Bond Options 462 21.5 Interest Rate Caps 464 21.6 European Swap Options 469 21.7 Term Structure Models 472 473 473 474 474 475 Chapter 22: Exotic Options and Other Nonstandard Products 477 22.1 Exotic Options 477 22.2 Agency Mortgage-Backed Securities 484
xj v Contents 22.3 Nonstandard Swaps 485 492 492 493 493 494 Chapter 23: Credit Derivatives 496 23.1 Credit Default Swaps 497 23.2 Valuation of Credit Default Swaps 501 23.3 Total Return Swaps 505 23.4 CDS Forwards and Options 506 23.5 Credit Indices 507 23.6 The Use of Fixed Coupons 507 23.7 Collateralized Debt Obligations 509 511 512 512 513 513 Chapter 24: Weather, Energy, and Insurance Derivatives 515 24.1 Weather Derivatives 515 24.2 Energy Derivatives 516 24.3 Insurance Derivatives 519 520 520 521 521 Further Question 522 Chapter 25: Derivatives Mishaps and What We Can Learn From Them 523 25.1 Lessons for All Users of Derivatives 523 25.2 Lessons for Financial Institutions 527 25.3 Lessons for Nonfinancial Corporations 532 534 534 Answers to Questions 535 Glossary of Terms 559 DerivaGem Software 577 Major Exchanges Trading Futures and Options 581 Table for N(x) When x < 0 582 Table for N(x) When x^0 583 Index 585