Measuring expectations in options markets: an application to the S&P500 index

Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In options markets, the most popular way has been to extract implied volatilities to assess the future variability of the underlying asset with the use of the Black-Scholes formula. In this manuscript, we propose a novel way to extract the whole time varying distribution of the market implied asset price from option prices. We use a Bayesian non-parametric method that makes use of the Sethuraman representation for Dirichlet processes to take into account the evolution of distributions in time. As an illustration, we present an analysis of options on the S&P500 index.