An Efficient GPU-Based Parallel Algorithm for Pricing Multi-Asset American Options

Abstract

We develop highly-efficient parallel Partial Differential Equation (PDE) based pricing methods on Graphics Processing Units (GPUs) for multi-asset American options. Our pricing approach is built upon a combination of a discrete penalty approach for the linear complementarity problem arising due to the free boundary and a GPU-based parallel Alternating Direction Implicit Approximate Factorization technique with finite differences on uniform grids for the solution of the linear algebraic system arising from each penalty iteration. A timestep size selector implemented efficiently on GPUs is used to further increase the efficiency of the methods. We demonstrate the efficiency and accuracy of the parallel numerical methods by pricing American options written on three assets.

Keywords: American Option, Multi-Asset, Penalty Method, Alternating Direction Implicit Approximate Factorization (ADI-AF), time adaptivity, Graphics Processing Units, GPUs, Parallel Computing, Finite Difference

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