High order combination technique for the efficient pricing of basket options

Abstract

In computational finance high dimensional problems typically arise,when pricing basket options, foreign-exchange (FX) options etc. Since the numberof grid points grows exponentially with the dimension, the so called curse of dimensionalityshows its eect very quickly. Sparse grids and the combination techniquehave proven their great ability to reduce the computational effort. In this article weintroduce a fourth order scheme for the combination technique to solve efficientlyhigh dimensional partial differential equation problems. In order to linearly combinethe sub-solutions, we propose a tensor-based interpolation method. We show thatour approach can preserve the error splitting structure of the sub-solutions and leadto a highly accurate sparse grid solution.