GPU based sparse grid technique for solving multidimensional options pricing PDEs

Abstract

It has been shown that the sparse grid combination technique can be a practical tool to solve high dimensional PDEs arising in multidimensional option pricing problems in finance. Hierarchical approximation of these problems leads to linear systems that are smaller in size compared to those arising from standard finite element or finite difference discretizations. However, these systems are still excessively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address iterative solutions via preconditioned Krylov subspace based methods, such as Stabilized BiConjugate Gradient (BiCGStab) and CG Squared (CGS), with the main focus on the design of such iterative solvers to harness massive parallelism of general purpose Graphics Processing Units (GPGPU)s. We discuss data structures and efficient implementation of iterative solvers. We also present a number of performance results to demonstrate the scalability of these solvers on the NVIDIA's CUDA platform.