Implicit Bayesian inference using option prices

A Bayesian approach to option pricing is presented in which posterior inference about the underlying returns process is conducted implicitly via observed option prices. A range of models allowing for conditional leptokurtosis, skewness and time‐varying volatility in returns are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Models are ranked according to several criteria, including out‐of‐sample predictive and hedging performance. The methodology accommodates heteroscedasticity and autocorrelation in the option pricing errors, as well as regime shifts across contract groups. The method is applied to intraday option price data on the S&P500 stock index for 1995. While the results provide support for models that accommodate leptokurtosis and skewness, no one model dominates when all criteria are considered.