Parallelizing a Black-Scholes solver based on finite elements and sparse grids

TLDR: The algorithmical structure of efficient algorithms operating on sparse grids are introduced, and it is demonstrated how they can be used to derive an efficient parallelization with OpenMP of the Black-Scholes solver.

Abstract: We present the parallelization of a sparse grid finite element discretization of the Black-Scholes equation, which is commonly used for option pricing. Sparse grids allow to handle higher dimensional options than classical approaches on full grids and can be extended to a fully adaptive discretization method. We introduce the algorithmical structure of efficient algorithms operating on sparse grids and demonstrate how they can be used to derive an efficient parallelization with OpenMP of the Black-Scholes solver. We show results on different commodity hardware systems based on multi-core architectures with up to 24 cores and discuss the parallel performance using Intel and Advanced Micro Devices AMD CPUs. Copyright © 2012 John Wiley & Sons, Ltd.