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

21 Pages Posted: 3 Apr 2010 Last revised: 2 Jan 2011

See all articles by Duy-Minh Dang

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Christina Christara

University of Toronto - Department of Computer Science

Kenneth R. Jackson

University of Toronto - Department of Computer Science

Date Written: March 28, 2010

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

Suggested Citation

Dang, Duy-Minh and Christara, Christina and Jackson, Kenneth R., A Parallel Implementation on GPUs of ADI Finite Difference Methods for Parabolic PDEs with Applications in Finance (March 28, 2010). Available at SSRN: https://ssrn.com/abstract=1580057 or http://dx.doi.org/10.2139/ssrn.1580057

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

Christina Christara

University of Toronto - Department of Computer Science ( email )

Department of Computer Science
University of Toronto
Toronto, Ontario M5S 3G4
Canada

Kenneth R. Jackson

University of Toronto - Department of Computer Science ( email )

Sandford Fleming Building
10 King's College Road, Room 3302
Toronto, Ontario M5S 3G4
Canada

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