Towards a Bayesian framework for option pricing

Abstract

In this paper, we describe a general method for constructing the posterior distribution of an option price. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. Our work extends that of Karolyi (1993) and Darsinos and Satchell (2001), but with the crucial difference that the likelihood function we use for inference is that which is directly implied by the underlying, rather than imposed in an ad hoc manner via the introduction of a function representing "measurement error." As such, an important problem still relevant for our method is that of model risk, and we address this issue by describing how to perform a Bayesian averaging of parameter inferences based on the different models considered using our framework.