Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous galerkin in time

Abstract

European basket options are priced by solving the multi-dimensional Black–Scholes–Merton equation. Standard numerical methods to solve these problems often suffer from the “curse of dimensionality”. We tackle this by using a dimension reduction technique based on a principal component analysis with an asymptotic expansion. Adaptive finite differences are used for the spatial discretization. In time we employ a discontinuous Galerkin scheme. The efficiency of our proposed method to solve a five-dimensional problem is demonstrated through numerical experiments and compared with a Monte-Carlo method.