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Measuring Expectations in Options Markets: An application to the S&P 500 Index

Extracting market expectations has always been an important issue when making national policies and investment decisions in financial markets. In option markets, the most popular way has been to extract implied volatilities to assess the future variability of the underlying 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 Bayesian nonparametric 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 the analysis of options on the S&P 500 index. This is joint work with Enrique Ter Horst from the Instituto de Estudios Superiores en Administracion, Venezuela.