Description
Book SynopsisThe Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance.
Table of ContentsPreface 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
