Abstract

Abstract The information content of a cross‐section of European option prices written on a given stock with a given time to maturity is summarized by the volatility smile. This article discusses how to graph the volatility smile, to interpret its asymmetry, convexity, term structure and time variation. Implied volatility, implied risk aversion, risk neutral valuation, and pricing kernels are discussed in the context of dynamic mixtures of geometric Brownian motions, possibly featuring stochastic volatility, long range dependence in volatility, and Poisson jumps. More general stochastic processes with possibly infinite activity jump processes as well as more data‐driven nonparametric approaches are also sketched.

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