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

Duy M. Dang, Christina Christara, Kenneth R. Jackson
University of Toronto – Department of Computer Science
Social Science Research Network Working Paper Series (03 April 2010)

@article{dangparallel,

   title={Parallel Implementation on GPUs of ADI Finite Difference Methods for Parabolic PDEs with Applications in Finance},

   author={Dang, D.M. and Christara, C. and Jackson, K.R.}

}

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We study the 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, as well as exotic long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with knockout features, under a cross-currency model with FX volatility skew. Numerical results showing the efficiency of the parallel methods are provided. In addition, we present an analysis of the impact of the FX volatility skew on the price of knockout PRDC swaps. This highlights the importance of having a realistic FX skew model in pricing and hedging exotic FX interest rate hybrids, in general, and PRDC swaps, in particular.
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