Hybrid parallel solutions of the Black-Scholes PDE with the truncated combination technique

Abstract

This paper presents an efficient approach to parallel pricing of multi-dimensional financial derivatives based on the Black-Scholes Partial Differential Equation (BS-PDE). One of the main challenges for such multi-dimensional problems is the curse of dimensionality, that is tackled in our approach by the combination technique (CT). This technique consists of a combination of several solutions obtained on anisotropic full grids. Hence, it offers the possibility to compute the BS-PDE on each one in an embarrassingly parallel way. Besides parallelizing on the CT level, we have developed a shared memory parallel multigrid solver for the BS-PDE. The parallel efficiency of our hybrid parallel approach is demonstrated by strong scaling results of 5D and 6D pricing problems.