Risk Neutral Densities: A Review

Trading in options with a wide range of exercise prices and a single maturity allows a researcher to extract the market's risk neutral probability density (RND) over the underlying price at expiration. The RND contains investors' beliefs about the true probabilities blended with their risk preferences, both of which are of great interest to academics and practitioners alike. With particular focus on U.S. equity options, this article reviews the historical development of this powerful concept, practical details of fitting an RND to option market prices, and the many ways in which investigators have tried to distill true expectations and risk premia from observed RNDs. I touch on areas of active current research including the "pricing kernel puzzle" and the "volatility surface," and offer thoughts on what has been learned about RNDs so far and fruitful directions for future research.