Profiling Neural Networks for option pricing

In recent years the problem of option pricing has received increasing interest from both financial institutions and academics. It is well known that conventional modeling techniques for option pricing have inherent, persistent and systematic biases which are mainly due to the assumption of constant volatility for prices associated with the underlying financial instrument. Nowadays, there is strong and increasing evidence that financial markets are far from being stationary and then, whenever dealing with option pricing, we have to take into account the market heteroschedasticity. A possible approach for dealing with non-constant volatility relies on the modeling of the basic characteristics named implied volatility. Unfortunately this task is extremely complex and parametric models are not available. In this paper the authors discuss how models from the class of Feedforward Neural Networks can be exploited for approaching the task of implied volatility modeling. In particular the paper shows how the main techniques from the nonlinear regression framework can be exploited when models from the class of Feedforward Neural Networks are used. Indeed, in such a case the paucity of data, which can be used for the network training, and the particular structure of Feedforward Neural Networks make the modeling task numerically complex. The authors discuss how the nonlinear regression technique named profile can be exploited for selecting the optimal network's structure and evaluating its numeical properties. To this end, a numerical procedure for empirical model building, in the case of Feedforward Neural Networks, has been developed. Results are evaluated through an ad-hoc procedure which utilizes the estimated implied volatility surface for pricing general contingent claims. Numerical experiments, in the case of the USD/DEM options, are presented and discussed.