CUDA implementation of barrier option valuation with jump-diffusion process and Brownian bridge

High Performance Computing on graphics processors (GPUs) has produced excellent results in a wide array of disciplines. Compute bound problems benefit from the massive parallelism and memory bound problems benefit from higher bandwidth and the ability to hide latency. In this work we apply GPU computing to a non-trivial option valuation problem to demonstrate its efficacy on problems with real world significance. Here we have focussed attention on barrier options modeled using an underlying jump-diffusion process and incorporating a Brownian bridge to account for inter-jump crossings. Exotic path-dependent options such as this often lack a closed-form solution and numerical methods must be used in their pricing. Monte Carlo methods which are commonly utilized involve simulation of the price trajectory along many independent paths, an approach that maps well to the GPU thread concept. Here we present the results of our CPU and GPU implementations comparing performance and providing details on both.

I. Introduction

As the pace of market trading has inevitably become more rapid and volume has grown, the need for fast accurate approaches to valuation of complex financial instruments has never been greater. In recent years, many disciplines have made effective use of GPUs for high performance computing. The energy industry for example has used GPUs to great effect for a variety of numerically intense problems arising from seismic imaging. The financial industry has also made use of GPUs. Monte Carlo valuation [1] in particular maps well to the architecture because the independent trajectories can be associated with independent threads. The purpose of this work is to evaluate the performance of GPU computing on a model with elevated complexity. We follow the methodology first proposed by Metwally and Atiya [2] which addresses barrier options using an underlying jump-diffusion process and a Brownian bridge to account for the probability of inter-jump barrier crossings. We have developed optimized CPU and GPU implementations of the algorithm described by Metwally and have compared the performance. Other groups have investigated this problem. The most closely related work is perhaps that of Johshi et. al. [3] who improved on the Metwally and Atiya work by using importance sampling and an analytic formula to reduce the variance. Joshi reports results for both log-normally and double exponential distributed jump sizes drawn at intervals according to a Poisson process. The time to standard error of 0.01 is reduced by up to a factor of 100 for low jump intensity. For higher jump intensity the method is as efficient as Metwally et al. We chose this particular problem because it is useful for evaluating the GPU performance on valuation problems of higher complexity and real world significance. A description of the model and details on the GPU implementation and results are presented herein.