An efficient graphics processing unit‐based parallel algorithm for pricing multi‐asset American options

Abstract

SUMMARY We develop highly efficient parallel 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 because of 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. Copyright © 2011 John Wiley & Sons, Ltd.