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Describe alternative ways of characterizing the volatility smile.

Describe the volatility smile for equity options and foreign currency options and provide possible explanations for its shape.

Describe the characteristics of foreign exchange rate distributions and their implications on option prices and implied volatility.

Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset price and to the pricing of options on the underlying asset.

Explain the implications of put-call parity on the implied volatility of call and put options.

Define volatility smile and volatility skew.

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.After completing this reading, you should be able to: 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.

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. Miller explain not just the mathematics but the ideas behind the models. Celebrated author and quant Emanuel Derman and Michael B. It is also a book about the principles of financial valuation and how to apply them. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. 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. 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. 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.