Following the Bayes path to option pricing

Conventional modeling techniques for option pricing have systematic biases resulting from the assumption of constant volatility (homoscedasticity ) for the price of the underlying asset. Nevertheless, practitioners seldom use stochastic v olatility models since the latter require making unverifiable assumptions about the price process. A different approach consists of “letting the data speak for itself”, i.e. to make a few general assum ptions about the process to be modeled, and to exploit the information available from the prices o f traded options. In this paper we develop a nonparametric model for specifying the volatility of t he underlying asset based on Feedforward Neural Networks and a Bayesian learning approach. We then develop an option-pricing model based on this volatility specification. Numerical experiment s are presented for the case of the USD/DEM options, accompanied by a graphical analysis of the resulting smiles.