Graphics processing unit pricing of exotic cross-currency interest rate derivatives with a foreign exchange volatility skew model

摘要

We present a graphics processing unit (GPU) parallelization of the computation of the price of exotic crosscurrencyrninterest rate derivatives via a partial differential equation (PDE) approach. In particular, we focusrnon the GPU-based parallel pricing of long-dated foreign exchange (FX) interest rate hybrids, namely powerrnreverse dual currency (PRDC) swaps with Bermudan cancelable features.We consider a three-factor pricingrnmodel with FX volatility skew, which results in a time-dependent parabolic PDE in three spatial dimensions.rnFinite difference methods on uniform grids are used for the spatial discretization of the PDE, and thernalternating direction implicit (ADI) technique is employed for the time discretization. We then exploit thernparallel architectural features of GPUs together with the Compute Unified Device Architecture frameworkrnto design and implement an efficient parallel algorithm for pricing PRDC swaps. Over each period of therntenor structure, we divide the pricing of a Bermudan cancelable PRDC swap into two independent pricingrnsubproblems, each of which can efficiently be solved on a GPU via a parallelization of the ADI timesteppingrntechnique. Numerical results indicate that GPUs can provide significant increase in performance over CPUsrnwhen pricing PRDC swaps. An analysis of the impact of the FX skew on such derivatives is provided.