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Sundaram & Das

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Derivatives: Principles and Practice
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  Derivatives:Principles andPractice Rangarajan K. Sundaram Stern School of  usiness New York UniversityNew  York NY 10012 Sanjiv R. Das Leavey School of  usiness Santa Clara UniversitySanta Clara CA 95053 I McGraw HillI Irwin  Contents Author Biographies  xv Preface  xvi Acknowledgments  xxi Chapter  1 Introduction  1 1.1  Forward and Futures Contracts  51.2  Options  9 -1.3  Swaps  101.4  Using Derivatives: Some Comments 1 5  The Structure of this Book  141.6  Exercises  15 11 PART ONE Futures and Forwards17Chapter  2 Futures Markets19 2.1 Introduction  19 2.2 The Changing Face of Futures Markets  19 2.3 The Functioning of Futures Exchanges  21 2.4 The Standardization of Futures Contracts  30 2.5 Closing Out Positions  34 2.6 Margin Requirements and Default Risk  36 2.7 Case Studies in Futures Markets  39 2.8 Exercises  53 Appendix 2A  Futures Trading and US Regulation:A Brief History  57 Chapter  3 Pricing Forwards and Futures I: The BasicTheory  60 3.1 Introduction  60 3.2 Pricing Forwards by Replication  61 3.3 Examples  63 3.4 Forward Pricing on Currencies and RelatedAssets  66 3.5 Forward-Rate Agreements  69 3.6 Concept Check  69 3.7 The Marked-to-Market Value of  a  ForwardContract  70 3.8 Futures Prices  72 3.9 Exercises  74 Appendix 3A  Compounding Frequency  79 Appendix 3B  Forward and Futures Prices withConstant Interest Rates  81 Appendix 3C  Rolling Over Futures Contracts  83 Chapter  4 Pricing Forwards and Futures II: Buildingon the Foundations 854 1  Introduction  85 4.2 From Theory to Reality  85 4.3 The Implied Repo Rate  89 4.4 Transactions Costs  92 4.5 Forward Prices and Future Spot Prices  92 4.6 Index Arbitrage  93 4.7 Exercises  97 Appendix 4A  Forward Prices with ConvenienceYields  100 Chapter  5 Hedging with Futures and Forwards101 5 1  Introduction  101 5.2 A Guide to the Main Results  103 5.3 The Cash Flow from  a  Hedged Position  104 5.4 The Case of No Basis Risk  105 5 5  The Minimum-Variance Hedge Ratio  106 5.6 Examples  109 5.7 Implementation  111 5.8 Further Issues in Implementation  112 5.9 Index Futures and Changing Equity Risk  114 5 10  Fixed-Income Futures and Duration-BasedHedging  115 5 11  Exercises  115 Appendix 5A  Derivation of the Optimal TailedHedge Ratio  h 120 Chapter  6 Interest-Rate Forwards and Futures 6.1 Introduction  122 6.2 Eurodollars and Libor Rates  122 6.3 Forward-Rate Agreements  123 6.4 Eurodollar Futures  129 122 viii  Contents  ix 6.5 Treasury Bond Futures 1366.6 Treasury Note Futures 1396.7 Treasury Bill Futures 1396.8 Duration-Based Hedging 1406.9 Exercises 143 Appendix 6A  Deriving the Arbitrage-FreeFRA Rate 147 Appendix 6B  PVBP-Based Hedging UsingEurodollar Futures 148 Appendix 6C  Calculating the ConversionFactor 149 Appendix 6D  Duration as a SensitivityMeasure 150 Appendix  6E  The Duration of  a  FuturesContract 151 PART TWO Options 153Chapter 7Options Markets155 7.1 Introduction 1557.2 Definitions and Terminology 155 7 3  Options as Financial Insurance 156 7 4  Naked Option Positions 158 7 5  Options as Views on Market Directionand Volatility 1627.6 Exercises 165 Appendix 7A  Options Markets 167 Chapter 8 Options: Payoffs and TradingStrategies 171 8.1 Introduction 1718.2 Trading Strategies I: Covered Calls andProtective Puts 1718.3 Trading Strategies II: Spreads 1748.4 Trading Strategies III: Combinations 1828.5 Trading Strategies IV: Other Strategies 1858.6 Which Strategies Are the Most WidelyUsed? 1898.7 The Barings Case 1898.8 Exercises 192 Appendix 8A  Asymmetric ButterflySpreads 195 Chapter 9 No-Arbitrage Restrictions on OptionPrices 196 9 1  Introduction 1969.2 Motivating Examples 196 9 3  Notation and Other Preliminaries 198 9 4  Maximum and Minimum Prices forOptions 199 9 5  The Insurance Value of an Option 2049.6 Option Prices and Contract Parameters 205 9 7  Numerical Examples 2089.8 Exercises 210 Chapter 1 Early Exercise and Put-Call Parity213 10 1  Introduction 21310.2 A Decomposition of Option Prices 213 10 3  The Optimality of Early Exercise 216 10 4  Put-Call Parity. 220 10 5  Exercises 226 Chapter 11 Option Pricing: An Introduction228 11 1  Overview 22811.2 The Binomial Model 229 11 3  Pricing by Replication in a One-PeriodBinomial Model 231 11 4  Comments 235 11 5  Riskless Hedge Portfolios 237 11 .6 Pricing Using Risk-NeutralProbabilities 238 11 7  The One-Period Model in GeneralNotation 24211.8 The Delta of an Option 242 11 9  An Application: Portfolio Insurance 246 11 10  Exercises 248 Appendix 11A  Riskless Hedge Portfoliosand Option Pricing 252 Appendix 11B  Risk-Neutral Probabilitiesand Arrow Security Prices 254 Appendix 11C  The Risk-Neutral Probability,No-Arbitrage, and MarketCompleteness 255 Appendix 11D  Equivalent MartingaleMeasures 257  x  Contents Chapter 12 Binomial Option Pricing259 12 1  Introduction 259 12 2  The Two-Period Binomial Tree 261 12 3  Pricing Two-Period European Options 262 12 4  European Option Pricing in General w-PeriodTrees 2691 2 5  Pricing American Options: PreliminaryComments 2691 2 6  American Puts on Non-Dividend-PayingStocks 2701 2 7  Cash Dividends in the Binomial Tree 2721 2 8  An Alternative Approach to CashDividends 2751 2 9  Dividend Yields in Binomial Trees 279 12 10  Exercises 282 Appendix 12A  A General Representation ofEuropean Option Prices 286 Chapter 13 Implementing the Binomial Model 289 13 1  Introduction 289 13 2  The Lognormal Distribution 289 13 3  Binomial Approximations of theLognormal 2941 3 4  Computer Implementation of the BinomialModel 298 13 5  Exercises 303 Appendix 13A  Estimating HistoricalVolatility 306 Chapter 14 The Black-Scholes Model308 14 1  Introduction 3081 4 2  Option Pricing in the Black-ScholesSetting 310 14 3  Remarks on the Formula 313 14 4  Working with the Formulae I: Plotting OptionPrices 3141 4 5  Working with the Formulae II: AlgebraicManipulation 3151 4 6  Dividends in the Black-Scholes Model 319 14 7  Options on Indices, Currencies,and Futures 324 14 8  Testing the Black-Scholes Model: ImpliedVolatility 327 14 9  The VIX and Its Derivatives 332 14 10  Exercises 335 Appendix 14A  Further Properties of theBlack-Scholes Delta 338 Appendix 14B  Variance and Volatility Swaps339 Chapter 15 The Mathematics of Black-Scholes 344 344 15 1  Introduction 344 15 2  Geometric Brownian Motion Defined 15 3  The Black-Scholes Formula viaReplication 3481 5 4  The Black-Scholes Formula via Risk-NeutralPricing 351 15 5  The Black-Scholes Formula via CAPM 353 15 6  Exercises 354 Chapter 16Options Modeling:Beyond Black-Scholes 357 16 1  Introduction 357 16 2  Jump-Diffusion Models 358 16 3  Stochastic Volatility 368 16 4  GARCH Models 374 16 5  Other Approaches 378 16 6  Implied Binomial Trees/Local VolatilityModels 379 16 7  Summary 389 16 8  Exercises 389 Appendix 16A  Program Code for Jump-Diffusions 393 Appendix 16B  Program Code for a StochasticVolatility Model 394 Appendix 16C  Heuristic Comments on OptionPricing under StochasticVolatility 396 Appendix 16D  Program Code for SimulatingGARCH Stock PricesDistributions 399 Appendix 16E  Local Volatility Models: The FourthPeriod of  the  Example 400 Chapter 17 Sensitivity Analysis: The Option Greeks 404 17 1  Introduction 4041 7 2  Interpreting the Greeks: A SnapshotView 404
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