Beyond implied volatility: extracting information from option prices

After a brief review of option pricing theory, we introduce various methods proposed for extracting the statistical information implicit in options prices. Among the methods discussed are: lognormal Edgeworth expansions, cumulant expansions, Hermite polynomial expansions, nonparametric kernel estimation of state price densities and maximum entropy methods. We discuss the advantages and drawbacks of each method, the interpretation of their results in economic terms, their theoretical consequences and their relevance for applications. The style is introductory and self-contained.