Bayesian inference for derivative prices

This paper develops a methodology for parameter and state variable inference using both asset and derivative price information. We combine theoretical pricing models and asset dynamics to generate a joint posterior for parameters and state variables and provide an MCMC simulation strategy for inference. There are several advantages of our inferential approach. First, more precise Parameter estimates are obtained when both asset and derivative price information are used. Second, we provide a diagnostic tool for model misspecification based on agreement of the state and parameter estimates with and without derivative price information. Furthermore, the time series properties of the state variables can also be used to evaluate model fit. We illustrate our methodology using daily equity index options on the Standard and Poor's (S&P 500) index from 1998-2002.