An artificial neural network representation of the SABR stochastic volatility model

Abstract

In this paper, the universal approximation theorem of artificial neural networks (ANNs) is applied to the stochastic alpha beta rho (SABR) stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al is considered, followed by the more accurate integration scheme of McGhee as well as a two-factor finite-difference scheme. The resulting ANN calculates 10 000 times faster than the finite-difference scheme while maintaining a high degree of accuracy. As a result, the ANN dispenses with the need for the commonly used SABR approximation.