  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.
