The Volatility Smile: An Introduction for Students and Practitioners (Hardcover)

Preface xi

Acknowledgments xiii

About the Authors xv

CHAPTER 1 Overview 1

CHAPTER 2 The Principle of Replication 13

CHAPTER 3 Static and Dynamic Replication 37

CHAPTER 4 Variance Swaps: A Lesson in Replication 57

CHAPTER 5 The P&L of Hedged Option Strategies in a Black-Scholes-Merton World 85

CHAPTER 6 The Effect of Discrete Hedging on P&L 105

CHAPTER 7 The Effect of Transaction Costs on P&L 117

CHAPTER 8 The Smile: Stylized Facts and Their Interpretation 131

CHAPTER 9 No-Arbitrage Bounds on the Smile 153

CHAPTER 10 A Survey of Smile Models 163

CHAPTER 11 Implied Distributions and Static Replication 175

CHAPTER 12 Weak Static Replication 203

CHAPTER 13 The Binomial Model and Its Extensions 227

CHAPTER 14 Local Volatility Models 249

CHAPTER 15 Consequences of Local Volatility Models 265

CHAPTER 16 Local Volatility Models: Hedge Ratios and Exotic Option Values 289

CHAPTER 17 Some Final Remarks on Local Volatility Models 303

CHAPTER 18 Patterns of Volatility Change 309

CHAPTER 19 Introducing Stochastic Volatility Models 319

CHAPTER 20 Approximate Solutions to Some Stochastic Volatility Models 337

CHAPTER 21 Stochastic Volatility Models: The Smile for Zero Correlation 353

CHAPTER 22 Stochastic Volatility Models: The Smile with Mean Reversion and Correlation 369

CHAPTER 23 Jump-Diffusion Models of the Smile: Introduction 383

CHAPTER 24 The Full Jump-Diffusion Model 395

Epilogue 417

APPENDIX A Some Useful Derivatives of the Black-Scholes-Merton Model 419

APPENDIX B Backward Itoˆ Integrals 421

APPENDIX C Variance Swap Piecewise-Linear Replication 431

Answers to End-of-Chapter Problems 433

References 497

Index 501