Pricing Barrier and American Options under the SABR model on the GPU

Abstract

In this paper, we present our study on using the GPU to accelerate the computation in pricing financial options. We first introduce the GPU programming and the SABR stochastic volatility model. We then discuss pricing options with quasi-Monte Carlo techniques under the SABR model. In particular, we focus on pricing barrier options by quasi-Monte Carlo and conditional probability correction methods and pricing American options by the least squares Monte Carlo method. We then present our GPU-based implementation for pricing barrier options and hybrid CPU-GPU implementation for pricing American options. In addition, we describe techniques for efficient use of GPU memory. We provide details of implementing these GPU numerical schemes for pricing options and compare performances of the GPU programs with their CPU counterparts. We find that GPU-based computing schemes can achieve 134X speedup for pricing barrier options while maintaining satisfactory pricing accuracy. For pricing American options, we also report that when the least squares Monte Carlo method is used, special techniques can be devised to use less GPU memory, resulting in 22X speedup, instead of the original 10X speedup.

Keywords: CUDA, SABR model, quasi-Monte Carlo, barrier options, American options, GPU memory usage

JEL Classification: C6, G12