Pricing high-dimensional Bermudan options using deep learning and higher-order weak approximation

Riu Naito and Toshihiro Yamada

Abstract

This paper proposes a new deep-learning-based algorithm for high-dimensional Bermudan option pricing. To the best of our knowledge, this is the first study of the arbitrary-order discretization scheme in Bermudan option pricing or dynamic programming problems. By discretizing the interval between early-exercise dates using a higher-order weak approximation of stochastic differential equations, it is possible to accurately approximate the price of Bermudan options. In particular, we provide the theoretical rate of convergence for the discretization of a Bermudan option price by utilizing the error analysis of the weak approximation of stochastic differential equations for the case of irregular payoff functions. This high-performance deep-learning method permits the conditional expectations appearing in Bermudan option pricing to be estimated quickly even if the dimension is high. The new approximation scheme is an alternative to the least squares regression method. Numerical examples for Bermudan option pricing in high-dimensional settings (including a 100-dimensional stochastic alpha–beta–rho model) demonstrate the validity of the proposed scheme.