Improving Neural Network Based Option Price Forecasting

As is widely known, the popular Black & Scholes model for option pricing suffers from systematic biases, as it relies on several highly questionable assumptions. In this paper we study the ability of neural networks (MLPs) in pricing call options on the S&P 500 index; in particular we investigate the effect of the hidden neurons in the in- and out-of-sample pricing. We modify the Black & Scholes model given the price of an option based on the no-arbitrage value of a forward contract, written on the same underlying asset, and we derive a modified formula that can be used for our purpose. Instead of using the standard backpropagation training algorithm we replace it with the Levenberg-Marquardt approach. By modifying the objective function of the neural network, we focus the learning process on more interesting areas of the implied volatility surface. The results from this transformation are encouraging.