A Highly Efficient Implementation on GPU Clusters of PDE-Based Pricing Methods for Path-Dependent Foreign Exchange Interest Rate Derivatives

17 Pages Posted: 23 Mar 2013 Last revised: 28 Apr 2013

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 20, 2013

Abstract

We present a highly efficient parallelization of the computation of the price of exotic cross-currency interest rate derivatives with path-dependent features via a Partial Differential Equation (PDE) approach. In particular, we focus on the parallel pricing on Graphics Processing Unit (GPU) clusters of long-dated foreign exchange (FX) interest rate derivatives, namely Power-Reverse Dual-Currency (PRDC) swaps with FX Target Redemption (FX-TARN) features under a three-factor model. Challenges in pricing these derivatives via a PDE approach arise from the high-dimensionality of the model PDE, as well as from path-dependency of the FX-TARN feature. The PDE pricing framework for FX-TARN PRDC swaps is based on partitioning the pricing problem into several independent pricing sub-problems over each time period of the swap's tenor structure, with possible communication at the end of the time period. Finite difference methods on non-uniform grids are used for the spatial discretization of the PDE, and the Alternating Direction Implicit (ADI) technique is employed for the time discretization. Our implementation of the pricing procedure on a GPU cluster involves (i) efficiently solving each independent sub-problems on a GPU via a parallelization of the ADI timestepping technique, and (ii) utilizing MPI for the communication between pricing processes at the end of the time period of the swap's tenor structure. Numerical results showing the efficiency of the parallel methods are provided.

Keywords: Power Reverse Dual Currency (PRDC) Swaps, Bermudan Cancelable, Partial Differential Equation (PDE), Alternating Direction Implicit (ADI), Finite Differences, Graphics Processing Units (GPUs), GPU Clusters, MPI, Parallel Computing

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

Suggested Citation

Dang, Duy-Minh and Christara, Christina and Jackson, Kenneth R., A Highly Efficient Implementation on GPU Clusters of PDE-Based Pricing Methods for Path-Dependent Foreign Exchange Interest Rate Derivatives (March 20, 2013). Available at SSRN: https://ssrn.com/abstract=2237718 or http://dx.doi.org/10.2139/ssrn.2237718

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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