The Volatility Smile

By Emanuel Derman and Michael B. Miller · Wiley · 2016

Study guide: Exam INV-201

A Wiley Finance book, written with contributions by David Park, that presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it, and is also a book about the principles of financial valuation and how to apply them. Its first half, Chapters 1 through 13, can serve as a standalone textbook on option valuation and the Black-Scholes-Merton model; the second half focuses on the behavior of the volatility smile.

On the syllabus

• Exam INV-201 — Chapter 8 (The Smile: Stylized Facts and Their Interpretation) and Chapter 10 (A Survey of Smile Models) for outcome 2j; Chapter 3 (Static and Dynamic Replication) for outcomes 3c and 3e; Chapter 5 (The P&L of Hedged Option Strategies in a Black-Scholes-Merton World) for outcomes 3c and 3d; Chapter 6 (The Effect of Discrete Hedging on P&L) and Chapter 7 (The Effect of Transaction Costs on P&L) for outcomes 3c and 3e.

Preface

Acknowledgments

About the Authors

1 Overview

2 The Principle of Replication

3 Static and Dynamic Replication

4 Variance Swaps: A Lesson in Replication

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

6 The Effect of Discrete Hedging on P&L

7 The Effect of Transaction Costs on P&L

8 The Smile: Stylized Facts and Their Interpretation

9 No-Arbitrage Bounds on the Smile

10 A Survey of Smile Models

11 Implied Distributions and Static Replication

12 Weak Static Replication

13 The Binomial Model and Its Extensions

14 Local Volatility Models

15 Consequences of Local Volatility Models

16 Local Volatility Models: Hedge Ratios and Exotic Option Values

17 Some Final Remarks on Local Volatility Models

18 Patterns of Volatility Change

19 Introducing Stochastic Volatility Models

20 Approximate Solutions to Some Stochastic Volatility Models

21 Stochastic Volatility Models: The Smile for Zero Correlation

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

23 Jump-Diffusion Models of the Smile: Introduction

24 The Full Jump-Diffusion Model

Epilogue

Appendix A Some Useful Derivatives of the Black-Scholes-Merton Model

Appendix B Backward Itô Integrals

Appendix C Variance Swap Piecewise-Linear Replication

Answers to End-of-Chapter Problems

References

Index

Sources

• The Volatility Smile (Wiley-VCH product page) — the publisher's contents list (the chapters, appendices and back matter, as printed there with page numbers), the authors, the ISBN of the October 2016 first edition, and the book description for the lead
• The Volatility Smile (Open Library record, LCCN 2016012191) — the catalogue's contents note, which gives the same twenty-four chapter titles, and the statement of responsibility ("with contributions by David Park")
• INV 201 Syllabus, Nov 2026/Mar 2027/Jul 2027 (SOA) — the chapters assigned and the learning outcomes