The Volatility Smile

The Volatility Smile provides an accessible account of both the classic Black-Scholes-Merton option model and the newer extensions of the model that have been developed over the past forty years. In contrast to textbooks that accentuate formality over intuition and understanding, The Volatility Smile explores both the ideas and the mathematics behind the models, walking a middle line between the rigor of the academic world and the practical insights of the trading desk. Based on a clear formulation of the principles of financial modeling, The Volatility Smile is also a book about how to evaluate and build financial models. Prior to the 1987 global stock market crash, the Black-Scholes-Merton option valuation model seemed to describe option markets reasonably well. Since the crash, however, equity index option markets have displayed a persistent volatility smile, in blatant disagreement with the Black-Scholes-Merton model. Quants around the world have labored over the preceding decades to extend the Black-Scholes-Merton model to accommodate this anomaly. Good financial models begin not with mathematics but with an understanding of the behavior of securities and markets. The first half of this book therefore focuses on the theory of option valuation, a study of the Black-Scholes-Merton model, illustrations of how to make practical use of it, and a discussion of its limitations. The second half provides an analysis of the empirical behavior of the volatility smile, and a detailed account of multiple ways in which the Black-Scholes-Merton model can be extended so as to rectify its inadequacies. In particular, the book provides a detailed account of the local volatility model, stochastic volatility models, and jump-diffusion.