Contents 

Preface ....................................................................................................................... 

Chapter 1: Introduction .................................................................................................. 1 

1.1 FuturesContracts .........................................................................................1 

1.2 HistoryofFutures Markets...........................................................................2 

1.3 The Over-the-Counter Market........................................................................4 

1.4 ForwardContracts........................................................................................6 

1.5 Options........................................................................................................7 

1.6 History of Options Markets......................................................................... 10 

1.7 Types ofTrader..........................................................................................11 

1.8 Hedgers ..................................................................................................... 11 

1.9 Speculators................................................................................................. 14 

1.10  Arbitrageurs............................................................................................... 17 

1.11  Dangers ..................................................................................................... 18  Summary ................................................................................................... 18  FurtherReading .........................................................................................20  Quiz.......................................................................................................... 20  PracticeQuestions....................................................................................... 20  FurtherQuestions .......................................................................................22 

Chapter 2: Futures Markets and Central Counterparties .................................................. 24 

2.1 Opening and ClosingFuturesPositions ........................................................ 24 

2.2 Speci.cationofaFuturesContract............................................................... 25 

2.3ConvergenceofFutures PricetoSpotPrice..................................................28 

2.4 The Operation ofMargin Accounts.............................................................. 29 

2.5 OTC Markets .............................................................................................32 

2.6 MarketQuotes ........................................................................................... 35 

2.7 Delivery..................................................................................................... 37 

2.8 TypesofTrader andTypesof Order............................................................38 

2.9 Regulation..................................................................................................39 

2.10  Accounting andTax ................................................................................... 40 

2.11  Forward vs.FuturesContracts.....................................................................42  Summary ................................................................................................... 44  FurtherReading .........................................................................................45  Quiz.......................................................................................................... 45  PracticeQuestions....................................................................................... 46  FurtherQuestions .......................................................................................47 

Chapter 3: Hedging Strategies Using Futures .................................................................. 49 

3.1 Basic Principles...........................................................................................49 

3.2 Arguments for and Against Hedging ............................................................52 

3.3 Basis Risk ..................................................................................................55 

3.4 Cross Hedging............................................................................................59 

3.5 Stock IndexFutures....................................................................................63 

3.6 Stack andRoll............................................................................................69  Summary....................................................................................................70  Further Reading..........................................................................................72  Quiz...........................................................................................................72  PracticeQuestions .......................................................................................73  FurtherQuestions .......................................................................................74  Appendix:ReviewofKeyConceptsin Statistics and theCAPM ....................76 

Chapter 4: Interest Rates .............................................................................................. 81 

4.1 Types of Rates............................................................................................81 

4.2 SwapRates.................................................................................................83 

4.3 The Risk-Free Rate.....................................................................................84 

4.4 Measuring Interest Rates .............................................................................85 

4.5 ZeroRates..................................................................................................87 

4.6 Bond Pricing ..............................................................................................88 

4.7 Determining Zero Rates ..............................................................................89 

4.8 ForwardRates............................................................................................93 

4.9 ForwardRateAgreements...........................................................................95 

4.10  Theoriesof theTerm Structureof InterestRates...........................................97  Summary.................................................................................................. 100  Further Reading........................................................................................101  Quiz.........................................................................................................101  PracticeQuestions ..................................................................................... 102  FurtherQuestions .....................................................................................103  Appendix: Exponential and LogarithmicFunctions..................................... 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 ForwardPrice for an Investment Asset.......................................................110 

5.5 Known Income.........................................................................................113 

5.6 Known Yield............................................................................................115 

5.7 ValuingForwardContracts........................................................................115 

5.8 AreForward Prices andFutures Prices Equal? ............................................ 118 

5.9 Futures Prices of Stock Indices.................................................................. 118 

5.10  Forward andFuturesContracts on Currencies.............................................121 

5.11  Futures onCommodities............................................................................124 

5.12  TheCost of Carry..................................................................................... 127 

5.13  Delivery Options.......................................................................................127 

5.14  Futures Prices and Expected Spot Prices.....................................................128  Summary.................................................................................................. 130  Further Reading........................................................................................131 

Contents  vii 

Quiz .........................................................................................................132  PracticeQuestions......................................................................................132  FurtherQuestions ......................................................................................134 

Chapter 6: Interest Rate Futures...................................................................................136 

6.1  DayCount andQuotationConventions.......................................................136 

6.2  Treasury BondFutures...............................................................................139 

6.3  EurodollarFutures.....................................................................................143 

6.4  Duration...................................................................................................148 

6.5  Duration-Based Hedging Strategies UsingFutures........................................152  Summary ..................................................................................................156  FurtherReading ........................................................................................157  Quiz .........................................................................................................157  PracticeQuestions......................................................................................158  FurtherQuestions ......................................................................................159 

Chapter 7: Swaps .......................................................................................................161 

7.1  Mechanics of Interest Rate Swaps...............................................................162 

7.2  DayCount Issues ......................................................................................167 

7.3  Con.rmations............................................................................................167 

7.4  TheComparative-Advantage Argument.......................................................168 

7.5  Valuationof InterestRateSwaps................................................................171 

7.6  How theValue Changes through Time........................................................174 

7.7  Fixed-for-Fixed Currency Swaps .................................................................175 

7.8  Valuation ofFixed-for-Fixed Currency Swaps ..............................................178 

7.9  Other Currency Swaps ...............................................................................180 

7.10  Credit Risk ...............................................................................................181 

7.11  Credit Default Swaps.................................................................................182 

7.12  OtherTypes of Swaps................................................................................183  Summary ..................................................................................................184  FurtherReading ........................................................................................185  Quiz .........................................................................................................185  PracticeQuestions......................................................................................186  FurtherQuestions ......................................................................................188 

Chapter 8: Securitization and the Credit Crisis of 2007 ..................................................190 

8.1  Securitization.............................................................................................190 

8.2  The U.S. HousingMarket..........................................................................194 

8.3 WhatWentWrong?...................................................................................198 

8.4  The Aftermath...........................................................................................200  Summary ..................................................................................................202  FurtherReading ........................................................................................202  Quiz .........................................................................................................203  PracticeQuestions......................................................................................203  FurtherQuestions ......................................................................................204 

Chapter 9: Mechanics of Options Markets ....................................................................205 

9.1  Types of Option ........................................................................................205 

9.2  OptionPositions........................................................................................208 

9.3  Underlying Assets......................................................................................210 

9.4  Speci.cation of Stock Options....................................................................211 

9.5 Trading ....................................................................................................215 

9.6 Commissions.............................................................................................216 

9.7 MarginRequirements................................................................................ 217 

9.8 The Options ClearingCorporation ............................................................. 219 

9.9 Regulation................................................................................................220 

9.10  Taxation...................................................................................................220 

9.11  Warrants, Employee Stock Options, andConvertibles..................................221 

9.12  Over-the-Counter Options Markets............................................................. 222  Summary.................................................................................................. 223  Further Reading........................................................................................223  Quiz.........................................................................................................224  PracticeQuestions ..................................................................................... 224  FurtherQuestions .....................................................................................225 

Chapter 10: Properties of Stock Options ...................................................................... 227 

10.1  Factors A.ecting Option Prices................................................................227 

10.2  Assumptions and Notation....................................................................... 231 

10.3  Upper and Lower Bounds for Option Prices.............................................. 232 

10.4  Put每CallParity....................................................................................... 235 

10.5  Calls ona Non-Dividend-Paying Stock..................................................... 239 

10.6  Puts ona Non-Dividend-Paying Stock ...................................................... 241 

10.7  E.ect of Dividends.................................................................................. 243  Summary................................................................................................ 244  FurtherReading ......................................................................................245  Quiz....................................................................................................... 245  PracticeQuestions.................................................................................... 246  FurtherQuestions....................................................................................247 

Chapter 11: Trading Strategies Involving Options .......................................................... 249 

11.1  Principal-Protected Notes......................................................................... 249 

11.2  Strategies Involvinga Single Option anda Stock....................................... 251 

11.3  Spreads................................................................................................... 253 

11.4  Combinations..........................................................................................261 

11.5  OtherPayo.s.......................................................................................... 264  Summary................................................................................................ 264  FurtherReading ......................................................................................265  Quiz....................................................................................................... 265  PracticeQuestions.................................................................................... 266  FurtherQuestions....................................................................................266 

Chapter 12: Introduction to Binomial Trees .................................................................. 268 

12.1  AOne-Step BinomialModel anda No-Arbitrage Argument.......................268 

12.2  Risk-NeutralValuation............................................................................ 272 

12.3  Two-StepBinomialTrees.........................................................................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 Numberof Time Steps....................................................... 281 

12.9  Using DerivaGem.................................................................................... 282 

Contents  ix 

12.10  Options on Other Assets...........................................................................282  Summary.................................................................................................287  Further Reading.......................................................................................287  Quiz........................................................................................................287  PracticeQuestions ....................................................................................288  FurtherQuestions....................................................................................289  Appendix: Derivation of the Black每Scholes每Merton Option Pricing  Formula from BinomialTree....................................................291 

Chapter 13: Valuing Stock Options: The Black每Scholes每Merton Model..........................293 

13.1  Assumptions about How Stock Prices Evolve.............................................294 

13.2  ExpectedReturn......................................................................................297 

13.3  Volatility.................................................................................................298 

13.4  EstimatingVolatilityfrom HistoricalData.................................................299 

13.5  Assumptions Underlying Black每Scholes每Merton .......................................301 

13.6  The Key No-Arbitrage Argument..............................................................302 

13.7  The Black每Scholes每MertonPricingFormulas............................................304 

13.8  Risk-NeutralValuation.............................................................................306 

13.9  ImpliedVolatilities...................................................................................307 

13.10  Dividends................................................................................................309  Summary.................................................................................................311  Further Reading.......................................................................................312  Quiz........................................................................................................313  PracticeQuestions ....................................................................................313  FurtherQuestions ....................................................................................315  Appendix: The Early Exercise of American Call Options on  Dividend-Paying Stocks ...........................................................316 

Chapter 14: Employee Stock Options ...........................................................................318 

14.1  Contractual Arrangements........................................................................318 

14.2  Do Options Align the Interests of Shareholders and Managers?...................320 

14.3  Accounting Issues....................................................................................321 

14.4  Valuation.................................................................................................323 

14.5  Backdating Scandals.................................................................................324  Summary.................................................................................................325  Further Reading.......................................................................................326  Quiz........................................................................................................326  PracticeQuestions ....................................................................................327  FurtherQuestions ....................................................................................327 

Chapter 15: Options on Stock Indices and Currencies.....................................................328 

15.1  Options on Stock Indices..........................................................................328 

15.2  Currency Options.....................................................................................331 

15.3  Options on StocksPaying Known Dividend Yields.....................................333 

15.4  Valuation of European Stock Index Options ..............................................335 

15.5  Valuation of European Currency Options ..................................................338 

15.6  American Options....................................................................................339  Summary.................................................................................................340  Further Reading.......................................................................................341  Quiz........................................................................................................341 

PracticeQuestions.................................................................................... 341  FurtherQuestions....................................................................................343 

Chapter 16: Futures Options and Black＊s Model............................................................ 344 

16.1  NatureofFutures Options ....................................................................... 344 

16.2  Reasons for thePopularityofFutures Options.......................................... 346 

16.3  European SpotandFutures Options......................................................... 347 

16.4  Put每CallParity.......................................................................................347 

16.5  Bounds forFutures Options..................................................................... 349 

16.6  AFuturesPrice as an AssetProviding a Yield........................................... 349 

16.7  Black＊sModel forValuingFutures Options............................................... 350 

16.8  Using Black＊s ModelInsteadof Black每Scholes每Merton............................. 350 

16.9  Valuation ofFutures Options Using BinomialTrees...................................351 

16.10  AmericanFutures Options vs. American Spot Options............................... 354 

16.11  Futures-Style Options..............................................................................354  Summary................................................................................................ 355  FurtherReading ......................................................................................356  Quiz....................................................................................................... 356  PracticeQuestions.................................................................................... 356  Further Questions....................................................................................357 

Chapter 17: The Greek Letters.................................................................................... 359 

17.1  Illustration.............................................................................................. 359 

17.2  Naked andCoveredPositions................................................................... 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  TheRealities of Hedging.......................................................................... 379 

17.11  Scenario Analysis.................................................................................... 379 

17.12  Extension ofFormulas............................................................................. 380 

17.13  Creating Options Synthetically forPortfolio Insurance............................... 382 

17.14  StockMarketVolatility............................................................................ 385  Summary................................................................................................ 385  FurtherReading ......................................................................................387  Quiz....................................................................................................... 387  PracticeQuestions.................................................................................... 388  Further Questions....................................................................................389 

Chapter 18: Binomial Trees in Practice ........................................................................ 391 

18.1  The Binomial Model fora 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 fora Dividend-Paying Stock..................................... 401 

18.4  Extensionsof the BasicTree Approach..................................................... 405 

18.5  Alternative Procedure forConstructingTrees............................................. 407 

18.6  Monte Carlo Simulation.......................................................................... 407 

Contents  xi 

Summary.................................................................................................409  Further Reading.......................................................................................410  Quiz........................................................................................................410  PracticeQuestions ....................................................................................411  FurtherQuestions....................................................................................412 

Chapter 19: Volatility Smiles .......................................................................................413 

19.1  Foreign Currency Options.........................................................................413 

19.2  Equity Options........................................................................................416 

19.3  TheVolatilityTerm Structure andVolatility Surfaces..................................418 

19.4  Whena Single Large JumpIs Anticipated.................................................420  Summary.................................................................................................421  Further Reading.......................................................................................422  Quiz........................................................................................................423  PracticeQuestions ....................................................................................423  FurtherQuestions....................................................................................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  TheVaR 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  EstimatingVolatilities andCorrelations......................................................446 

20.7  Comparison of Approaches.......................................................................451 

20.8  BackTesting ............................................................................................452  Summary.................................................................................................452  Further Reading.......................................................................................453  Quiz........................................................................................................453  PracticeQuestions ....................................................................................454  FurtherQuestions....................................................................................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  EuropeanSwap Options...........................................................................469 

21.7  Term Structure Models.............................................................................472  Summary.................................................................................................473  Further Reading.......................................................................................473  Quiz........................................................................................................474  PracticeQuestions ....................................................................................474  FurtherQuestions....................................................................................475 

Chapter 22: Exotic Options and Other Nonstandard Products .........................................477 

22.1  Exotic Options.........................................................................................477 

22.2  Agency Mortgage-Backed Securities ..........................................................484 

22.3  Nonstandard Swaps................................................................................. 485  Summary................................................................................................ 492  FurtherReading ......................................................................................492  Quiz....................................................................................................... 493  PracticeQuestions.................................................................................... 493  FurtherQuestions....................................................................................494 

Chapter 23: Credit Derivatives..................................................................................... 496 

23.1  Credit Default Swaps............................................................................... 497 

23.2  Valuation of Credit Default Swaps............................................................501 

23.3  TotalReturn Swaps.................................................................................505 

23.4  CDSForwards and Options..................................................................... 506 

23.5  Credit Indices.......................................................................................... 507 

23.6  The Use ofFixedCoupons ...................................................................... 507 

23.7  Collateralized Debt Obligations ................................................................509  Summary................................................................................................ 511  FurtherReading ......................................................................................512  Quiz....................................................................................................... 512  PracticeQuestions.................................................................................... 513  FurtherQuestions....................................................................................513 

Chapter 24: Weather, Energy, and Insurance Derivatives ................................................ 515 

24.1  Weather Derivatives.................................................................................515 

24.2  Energy Derivatives................................................................................... 516 

24.3  Insurance Derivatives............................................................................... 519  Summary................................................................................................ 520  FurtherReading ......................................................................................520  Quiz....................................................................................................... 521  PracticeQuestions.................................................................................... 521  FurtherQuestion .....................................................................................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 forFinancial Institutions ............................................................. 527 

25.3  Lessons for Non.nancialCorporations ..................................................... 532  Summary................................................................................................ 534  FurtherReading ......................................................................................534 

Answers to Quiz Questions............................................................................................ 535  Glossary of Terms........................................................................................................ 535  DerivaGem Software .................................................................................................... 535  Major Exchanges Trading Futures and Options............................................................... 535  Table for NexT .................. ........................................................................................... 535