Bayesian Inference for Derivative Prices
Nicholas G. Polson, Jonathan R. Stroud
University of Chicago and University of Pennsylvania
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. Secondly, 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.
The manuscript is available in PDF format.