Financial option valuation by unsupervised learning with artificial neural networks

TL;DR

This paper explores using unsupervised artificial neural networks to solve PDEs for pricing European and American financial options, providing a flexible alternative to traditional numerical methods and extending to high-dimensional exotic options.

Contribution

It introduces an ANN-based unsupervised learning approach for option valuation, capable of handling high-dimensional problems and American options without traditional numerical schemes.

Findings

ANN accurately prices European options with low error

Method effectively handles American options via complementarity formulation

High-dimensional exotic options are computed with good accuracy

Abstract

Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black-Scholes equation, whereas for the American option, we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements).