The option pricing model based on time values: an application of the universal approximation theory on unbounded domains

TL;DR

This paper introduces a new decision function for option pricing that leverages universal approximation theory, leading to faster convergence and improved generalization in neural network models.

Contribution

It presents a novel universal approximation theorem for the decision function on unbounded domains, enhancing neural network-based option pricing models.

Findings

Faster convergence in numerical experiments

Improved generalization performance

Theoretical proof of universal approximation on unbounded domains

Abstract

We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio. In numerical experiments, the new decision function significantly improves the original model of Hutchinson-Lo-Poggio with faster convergence and better generalization performance. By proving a novel universal approximation theorem, we show that our decision function rather than Hutchinson-Lo-Poggio's can be approximated on the entire domain of definition by neural networks. Thus the experimental results are partially explained by the representation properties of networks.