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.