The Volatility Smile: An Introduction for Students and Practitioners

by Emanuel Derman, Michael B. Miller, David Park (Contributor)

The 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. Despite this success, the model is fundamentally at odds with the observed behavior of option 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

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 The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.

Genres: Finance, Textbooks

495 pages, Kindle Edition

First published March 7, 2016

About the author

Emanuel Derman (born c. 1945) is a Jewish South African-born academic, businessman and writer. He is best known as a quantitative analyst, and author of the book My Life as a Quant: Reflections on Physics and Finance

Reviews

[Frederik Skjott · Rating 4 out of 5]

As part of a university course on options, we were encouraged to use this book. I read it twice. It has a nice and steady flow, which is a wonderful break from other theorem/proof/lemma that many continuous finance books use. I was particularly intrigued by the section on replicating a barrier option using a series of vanilla.

[Evan · Rating 4 out of 5]

Thought this was a strong textbook. Although I do not have substantial experience with other books on option pricing, I felt Derman was highly thorough and clear. I appreciated the effort Derman takes to make intuitive sense of derived results, as well as the frequent discussion of the potential discrepancies between models discussed and the behavior of real markets.

[Chris McRobbie · Rating 4 out of 5]

two brilliant minds in finance that had a great impact on how the game was developed and is played.

[Jovany Agathe · Rating 2 out of 5]

Emanuel Derman’s “The Volatility Smile” is an excellent book for those who have learned something about derivatives and now need to think on their own.
More than just repeating known formulas and theorems, the author is always careful to distinguish between theories and models, alternating concepts and practice (including end-of-chapter exercises).