Pricing of cross-currency interest rate derivatives on Graphics Processing Units

Abstract

We present a Graphics Processing Unit (GPU) parallelization of the computation of the price of cross-currency interest rate derivatives via a Partial Differential Equation (PDE) approach. In particular, we focus on the GPU-based parallel computation of the price of long-dated foreign exchange interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. We consider a three-factor pricing model with foreign exchange skew which results in a time-dependent parabolic PDE in three spatial dimensions. Finite difference methods on uniform grids are used for the spatial discretization of the PDE, and the Alternating Direction Implicit (ADI) technique is employed for the time discretization. We then exploit the parallel architectural features of GPUs together with the Compute Unified Device Architecture (CUDA) framework to design and implement an efficient parallel algorithm for pricing PRDC swaps. Over each period of the tenor structure, we divide the pricing of a Bermudan cancelable PRDC swap into two independent pricing subproblems, each of which can efficiently be solved on a GPU via a parallelization of the ADI scheme at each timestep. Using this approach on two NVIDIA Tesla C870 GPUs of an NVIDIA 4-GPU Tesla S870 to price a Bermudan cancelable PRDC swap having a 30 year maturity and annual exchange of fund flows, we have achieved an asymptotic speedup by a factor of 44 relative to a single thread on a 2.0GHz Xeon processor.