An Artificial Neural Network Representation of the SABR Stochastic Volatility Model

Abstract

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate integration scheme of McGhee [2011] as well as a two factor finite difference scheme. The resulting ANN calculates 10,000 times faster than the finite difference scheme whilst maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR Approximation.

Keywords: Stochastic Volatility, SABR Model, SABR Approximation, SABR Integration Scheme, Artificial Neural Network, Universal Approximation Theorem

JEL Classification: C13, C15, C44, C51, C52, C63, D40, G12, G13, G15, G21, G28, K22, M40