The volatility smile
By: Emanuel Derman, Michael B. Miller ; with contributions by David Park
Contributors: Miller, Michael B. (Michael Bernard), 1973- author; Park, David, contributor
Series: The Wiley finance series; Wiley finance series
Published: 2016
Language: eng
Number of pages: 512
ISBN-13: 9781118959169
Subjects: Securities; Mathematical models; Valuation; Finance
Description: "The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options model was the greatest innovation of 20th Century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel€Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models"--
Notes: Includes bibliographical references (pages 497-499) and index.
Table of contents: title: Machine generated contents note: Preface About the Authors Chapter 1: Overview Chapter 2: The Principle of Replication Chapter 3: Static and Dynamic Replication Chapter 4: Variance Swaps: A Lesson in Replication Chapter 5: The P & L of Hedged Option Strategies in a Black-Scholes-Merton World Chapter 6: The Effect of Discrete Hedging on P & L Chapter 7: The Effect of Transactions Costs on P & L Chapter 8: The Smile: Stylized Facts and Their Interpretation Chapter 9: No-Arbitrage Bounds on the Smile Chapter 10: A Survey of Smile Models Chapter 11: Implied Distributions and Static Replication Chapter 12: Weak Static Replication Chapter 13: The Binomial Model and Its Extensions Chapter 14: Local Volatility Models Chapter 15: Consequences of Local Volatility Models Chapter 16: Local Volatility Models: Hedge Ratios and Exotic Option Values Chapter 17: Some Final Remarks on Local Volatility Models Chapter 18: Patterns of Volatility Change Chapter 19: Introducing Stochastic Volatility Models Chapter 20: Approximate Solutions to Some Stochastic Volatility Models Chapter 21: Stochastic Volatility Models: The Smile for Zero Correlation Chapter 22: Stochastic Volatility Models: The Smile with Mean Reversion and Correlation Chapter 23: Jump-Diffusion Models of the Smile: Introduction Chapter 24: The Full Jump-Diffusion Model Appendix A: Some Useful Derivatives of the Black-Scholes-Merton Model Appendix B: Backward It & ocirc; Integrals References Answers to End-of-Chapter Problems Index.