1Bayesian Analysis of the Black-Scholes Option Price

This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness both in the price process and in volatility to derive the prior and posterior densities of a European call option. Expressions for the density of the option price conditional on the sample estimate of volatility and on the asset price respectively, are also derived. Numerical results are presented to compare how the dispersion of the option price changes in the transition from prior to posterior information, where information may be price or sample variance or both. The derived expression for the posterior density is of considerable interest since it can be straightforwardly combined with a loss function to produce optimal estimates of options prices