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Contents Preface xiii Chapter 1: Introduction 1 Futures Contracts 1 History of Futures Markets 2 The Over-the-Counter Market. 4 Forward Contracts 6 Options 7 History of Options Markets 10 Types of Trader 11 Hedgers 11 Speculators 14 Arbitrageurs 17 Dangers 18 Summary 18 Further Reading 20 Quiz 20 Practice Questions 20 Further Questions 22 Chapter 2: Futures Markets and Central Counterparties 24 Opening and Closing Futures Positions 24 Speci?cation of a Futures Contract. 25 Convergence of Futures Price to Spot Price 28 The Operation of Margin Accounts 29 OTC Markets 32 Market Quotes 35 Delivery 37 Types of Trader and Types of Order 38 Regulation 39 Accounting and Tax 40 Forward vs. Futures Contracts 42 Summary 44 Further Reading 45 Quiz 45 Practice Questions 46 Further Questions 47 v _x00C_vi Contents Chapter 3: Hedging Strategies Using Futures 49 Basic Principles 49 Arguments for and Against Hedging 52 Basis Risk 55 Cross Hedging 59 Stock Index Futures 63 Stack and Roll 69 Summary 70 Further Reading 72 Quiz 72 Practice Questions 73 Further Questions 74 Appendix: Review of Key Concepts in Statistics and the CAPM 76 Chapter 4: Interest Rates 81 Types of Rates 81 Swap Rates 83 The Risk-Free Rate 84 Measuring Interest Rates 85 Zero Rates 87 Bond Pricing 88 Determining Zero Rates 89 Forward Rates 93 Forward Rate Agreements 95 Theories of the Term Structure of Interest Rates 97 Summary 100 Further Reading 101 Quiz 101 Practice Questions 102 Further Questions 103 Appendix: Exponential and Logarithmic Functions 105 Chapter 5: Determination of Forward and Futures Prices 107 Investment Assets vs. Consumption Assets 107 Short Selling 108 Assumptions and Notation 109 Forward Price for an Investment Asset 110 Known Income 113 Known Yield 115 Valuing Forward Contracts 115 Are Forward Prices and Futures Prices Equal? 118 Futures Prices of Stock Indices 118 Forward and Futures Contracts on Currencies 121 Futures on Commodities 124 The Cost of Carry 127 Delivery Options 127 Futures Prices and Expected Spot Prices 128 Summary 130 Further Reading 131 _x00C_Contents vii Quiz 132 Practice Questions 132 Further Questions 134 Chapter 6: Interest Rate Futures. 136 Day Count and Quotation Conventions 136 Treasury Bond Futures 139 Eurodollar Futures. 143 Duration 148 Duration-Based Hedging Strategies Using Futures 152 Summary 156 Further Reading 157 Quiz 157 Practice Questions 158 Further Questions 159 Chapter 7: Swaps 161 Mechanics of Interest Rate Swaps 162 Day Count Issues 167 Con?rmations 167 The Comparative-Advantage Argument 168 Valuation of Interest Rate Swaps 171 How the Value Changes through Time 174 Fixed-for-Fixed Currency Swaps 175 Valuation of Fixed-for-Fixed Currency Swaps 178 Other Currency Swaps 180 Credit Risk 181 Credit Default Swaps 182 Other Types of Swaps 183 Summary 184 Further Reading 185 Quiz 185 Practice Questions 186 Further Questions 188 Chapter 8: Securitization and the Credit Crisis of 2007 190 Securitization 190 The U.S. Housing Market 194 What Went Wrong? 198 The Aftermath 200 Summary 202 Further Reading 202 Quiz 203 Practice Questions 203 Further Questions 204 Chapter 9: Mechanics of Options Markets 205 Types of Option 205 Option Positions 208 Underlying Assets 210 Speci?cation of Stock Options 211 _x00C_viii Contents Trading 215 Commissions. 216 Margin Requirements 217 The Options Clearing Corporation 219 Regulation 220 Taxation 220 Warrants, Employee Stock Options, and Convertibles 221 Over-the-Counter Options Markets 222 Summary 223 Further Reading 223 Quiz 224 Practice Questions 224 Further Questions 225 Chapter 10: Properties of Stock Options 227 Factors A?ecting Option Prices 227 Assumptions and Notation 231 Upper and Lower Bounds for Option Prices 232 Put¨CCall Parity 235 Calls on a Non-Dividend-Paying Stock 239 Puts on a Non-Dividend-Paying Stock 241 E?ect of Dividends 243 Summary 244 Further Reading 245 Quiz 245 Practice Questions 246 Further Questions 247 Chapter 11: Trading Strategies Involving Options 249 Principal-Protected Notes 249 Strategies Involving a Single Option and a Stock 251 Spreads 253 Combinations 261 Other Payo?s 264 Summary 264 Further Reading 265 Quiz 265 Practice Questions 266 Further Questions 266 Chapter 12: Introduction to Binomial Trees 268 A One-Step Binomial Model and a No-Arbitrage Argument 268 Risk-Neutral Valuation 272 Two-Step Binomial Trees 274 A Put Example 277 American Options 278 Delta 279 Determining u and d 280 Increasing the Number of Time Steps 281 Using DerivaGem 282 _x00C_Contents ix Options on Other Assets 282 Summary 287 Further Reading 287 Quiz 287 Practice Questions 288 Further Questions 289 Appendix: Derivation of the Black¨CScholes¨CMerton Option Pricing Formula from Binomial Tree 291 Chapter 13: Valuing Stock Options: The Black¨CScholes¨CMerton Model 293 Assumptions about How Stock Prices Evolve 294 Expected Return 297 Volatility 298 Estimating Volatility from Historical Data 299 Assumptions Underlying Black¨CScholes¨CMerton 301 The Key No-Arbitrage Argument 302 The Black¨CScholes¨CMerton Pricing Formulas 304 Risk-Neutral Valuation 306 Implied Volatilities 307 Dividends 309 Summary 311 Further Reading 312 Quiz 313 Practice Questions 313 Further Questions 315 Appendix: The Early Exercise of American Call Options on Dividend-Paying Stocks 316 Chapter 14: Employee Stock Options 318 Contractual Arrangements 318 Do Options Align the Interests of Shareholders and Managers? 320 Accounting Issues 321 Valuation 323 Backdating Scandals 324 Summary 325 Further Reading 326 Quiz 326 Practice Questions 327 Further Questions 327 Chapter 15: Options on Stock Indices and Currencies 328 Options on Stock Indices 328 Currency Options 331 Options on Stocks Paying Known Dividend Yields 333 Valuation of European Stock Index Options 335 Valuation of European Currency Options 338 American Options 339 Summary 340 Further Reading 341 Quiz 341 _x00C_x Contents Practice Questions 341 Further Questions 343 Chapter 16: Futures Options and Black's Model 344 Nature of Futures Options 344 Reasons for the Popularity of Futures Options 346 European Spot and Futures Options 347 Put¨CCall Parity 347 Bounds for Futures Options 349 A Futures Price as an Asset Providing a Yield. 349 Black's Model for Valuing Futures Options 350 Using Black's Model Instead of Black¨CScholes¨CMerton 350 Valuation of Futures Options Using Binomial Trees 351 American Futures Options vs. American Spot Options 354 Futures-Style Options 354 Summary 355 Further Reading 356 Quiz 356 Practice Questions 356 Further Questions 357 Chapter 17: The Greek Letters 359 Illustration 359 Naked and Covered Positions 360 Greek Letter Calculation 362 Delta 363 Theta 369 Gamma 371 Relationship Between Delta, Theta, and Gamma 374 Vega 378 17.9 Rho 377 The Realities of Hedging 379 Scenario Analysis 379 Extension of Formulas 380 Creating Options Synthetically for Portfolio Insurance 382 Stock Market Volatility 385 Summary 385 Further Reading 387 Quiz 387 Practice Questions 388 Further Questions 389 Chapter 18: Binomial Trees in Practice 391 The Binomial Model for a Non-Dividend-Paying Stock 391 Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts 398 The Binomial Model for a Dividend-Paying Stock 401 Extensions of the Basic Tree Approach 405 Alternative Procedure for Constructing Trees 407 Monte Carlo Simulation 407 _x00C_Contents xi Summary 409 Further Reading 410 Quiz 410 Practice Questions 411 Further Questions 412 Chapter 19: Volatility Smiles 413 Foreign Currency Options 413 Equity Options 416 The Volatility Term Structure and Volatility Surfaces 418 When a Single Large Jump Is Anticipated 420 Summary 421 Further Reading 422 Quiz 423 Practice Questions 423 Further Questions 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 The VaR and ES Measures 428 Historical Simulation 431 Model-Building Approach 436 Generalization of Linear Model 439 Quadratic Model 444 Estimating Volatilities and Correlations 446 Comparison of Approaches 451 Back Testing 452 Summary 452 Further Reading 453 Quiz 453 Practice Questions 454 Further Questions 455 Chapter 21: Interest Rate Options 458 Exchange-Traded Interest Rate Options 458 Embedded Bond Options 460 Black's Model 460 European Bond Options 462 Interest Rate Caps 464 European Swap Options 469 Term Structure Models 472 Summary 473 Further Reading 473 Quiz 474 Practice Questions 474 Further Questions 475 Chapter 22: Exotic Options and Other Nonstandard Products 477 Exotic Options 477 Agency Mortgage-Backed Securities 484 _x00C_xii Contents Nonstandard Swaps 485 Summary 492 Further Reading 492 Quiz 493 Practice Questions 493 Further Questions 494 Chapter 23: Credit Derivatives 496 Credit Default Swaps 497 Valuation of Credit Default Swaps 501 Total Return Swaps 505 CDS Forwards and Options 506 Credit Indices 507 The Use of Fixed Coupons 507 Collateralized Debt Obligations 509 Summary 511 Further Reading 512 Quiz 512 Practice Questions 513 Further Questions 513 Chapter 24: Weather, Energy, and Insurance Derivatives 515 Weather Derivatives 515 Energy Derivatives 516 Insurance Derivatives 519 Summary 520 Further Reading 520 Quiz 521 Practice Questions 521 Further Question 522 Chapter 25: Derivatives Mishaps and What We Can Learn From Them 523 Lessons for All Users of Derivatives 523 Lessons for Financial Institutions 527 Lessons for Non?nancial Corporations 532 Summary 534 Further Reading 534 Answers to Quiz Questions 535 Glossary of Terms 535 DerivaGem Software 535 Major Exchanges Trading Futures and Options 535 Table for NexT 535