A Parallel Implementation on GPUs of ADI Finite Difference Methods for Parabolic PDEs with Applications in Finance

Abstract

We study a parallel implementation on a Graphics Processing Unit (GPU) of Alternating Direction Implicit (ADI) time-discretization methods for solving time-dependent parabolic Partial Differential Equations (PDEs) in three spatial dimensions with mixed spatial derivatives in a variety of applications in computational finance. Finite differences on uniform grids are used for the spatial discretization of the PDEs. As examples, we apply the GPU-based parallel methods to price European rainbow and European basket options, each written on three assets. Numerical results showing the efficiency of the parallel methods are provided.

Keywords: Alternating Direction Implicit, ADI, Partial Differential Equation, PDE, Graphics Processing Units, GPUs, parallel computing, finite difference, multi-asset options

JEL Classification: E40, E43, G12, G13, C61, C63