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

Concurrency and Computation: Practice and Experience, 2011

15 Pages Posted: 4 Aug 2010 Last revised: 10 Apr 2011

See all articles by Yu Tian

Yu Tian

Monash University

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation)

Fima Klebaner

Monash University

Kais Hamza

Monash University

Date Written: March 28, 2011

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

Suggested Citation

Tian, Yu and Zhu, Zili and Klebaner, Fima and Hamza, Kais, Pricing Barrier and American Options under the SABR model on the GPU (March 28, 2011). Concurrency and Computation: Practice and Experience, 2011, Available at SSRN: https://ssrn.com/abstract=1653166

Yu Tian (Contact Author)

Monash University ( email )

Melbourne, Victoria VIC 3800
Australia

Zili Zhu

Government of the Commonwealth of Australia - CSIRO (Commonwealth Scientific and Industrial Research Organisation) ( email )

Gate 5 Normanby Road
Clayton
Melbourne, Australian Capital Territory 3168
Australia
61 3 95458003 (Phone)
61 3 9545 8080 (Fax)

Fima Klebaner

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

Kais Hamza

Monash University ( email )

23 Innovation Walk
Wellington Road
Clayton, Victoria 3800
Australia

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