Following the Bayes approach to option pricing
Marco Avellaneda, Andrea Carelli and Fabio Stella

Conventional modeling techniques for option pricing have systematic biases resulting from the  assumption of constant volatility (homoskedasticity) for the price of the underlying asset. Nevertheless, practitioners seldom use stochastic volatility models since the latter require making unverifiable assumptions about the  price process. A different approach consists in ``letting the data speak for itself''. i.e. to make  a few general assumptions  about the process to be modeled and to exploit the information available from  the prices of traded  options. In this paper,  we develop a non-parametric model  for specifying the volatility of the underlying asset based on Feedforward Neural Networkds and a Bayesian learning approach. We then develep an option pricing model based on this volatility sepcification. Numerical experiments are presented for the case of USD/DEM options , accompanied by a graphical analysis of the resulting smiles.