GPU Pricing of Exotic Cross-Currency Interest Rate Derivatives with a Foreign Exchange Volatility Skew Model

Abstract

We present a Graphics Processing Unit (GPU) parallelization of the computation of the price of exotic cross-currency interest rate derivatives via a Partial Differential Equation (PDE) approach. In particular, we focus on the GPU-based parallel pricing of long-dated foreign exchange (FX) interest rate hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. We consider a three-factor pricing model with FX volatility 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 timestepping technique. Numerical results indicate that GPUs can provide significant increase in performance over CPUs when pricing PRDC swaps. An analysis of the impact of the FX skew on such derivatives is provided.

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

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