HETEROGENEOUS COMPUTATION OF RAINBOW OPTION PRICES USING FOURIER COSINE SERIES EXPANSION UNDER A MIXED CPU–GPU COMPUTATION FRAMEWORK

• Published date: 01 April 2014
• Author: A. Cassagnes,H. Ohashi,Y. Chen
• DOI: http://doi.org/10.1002/isaf.1349
• Date: 01 April 2014

HETEROGENEOUS COMPUTATION OF RAINBOW OPTION PRICES

USING FOURIER COSINE SERIES EXPANSION UNDER

A MIXED CPU–GPU COMPUTATION FRAMEWORK

A. CASSAGNES,

a

*Y. CHEN

a,b

AND H. OHASHI

b

a

Department of Human and Engineered EnvironmentalStudies, Graduate School of Frontier Sciences, The University of Tokyo,

113-8656 Tokyo, Japan

b

Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo113-8656, Japan

SUMMARY

This paper focuses on comparing different heterogeneous computational designs for the calculation of rainbow

options prices using the Fourier-cosine series expansion (COS) method. We also propose a simple enough way

to automatically decide the ratio of load balancing at runtime. A general-purpose computing on graphic processing

unit implementation of the two-dimensional composite Simpson rule free of conditional statements with some de-

gree of loop unrolling is also introduced. We will also show how to reduce the integration domain of coefficients

appearing in the option pricing and by doing so achieve a substantial speed-up and improve accuracy when com-

pared with a straightforward implementation. Copyright © 2014 John Wiley & Sons, Ltd.

Keywords: exotic options; GPGPU; distributed computation

1. INTRODUCTION

The option pricing problem is connected to the estimation of a no-arbitrage price for financial deriva-

tives. For simple enough products such as European vanilla options, closed-form solutions exist and are

mostly the results of the celebrated Black–Scholes formula (Black & Scholes, 1973). More involved

problems, such as the pricing of American, exotic or high-dimensional derivatives, often rely on trans-

form methods such as the Fourier, Laplace or Gauss to handle their increasing complexity (Carr, Madan

& Smith, 1999; Broadie & Yamamoto, 2003; Dufresne, Garrido & Morales, 2009). Readers interested

in a more complete and technical introduction to the financial asset pricing theory, including American

options pricing using Markov chain approximation, are redirected to Protter (2001) and Simonato

(2011). Because of increasingly complex products that are handled on a daily basis by the financial in-

dustry, tangentially occurring with the rise of big data problematics, requirements in sheer computa-

tional force are expected to increase over time.

General-purpose computing on graphic processing units (GPGPUs) is a term that encompasses tech-

niques and concepts relevant to the use of graphic processing units (GPUs) in distribution of computa-

tional load. GPUs traditionally used for the rendering of graphics on home computers are, by design,

many-cores architectures fit for distributed computing. As such, they proved to be viable hardware plat-

forms for computationally heavy tasks with significant data parallelism. It has been shown to provide

speed-up factors customarily tenfolds when compared with a traditional standalone central processing

* Correspondence to: A. CASSAGNES, Department of Human and Engineered Environmental Studies, Graduate School of

Frontier Sciences, The University of Tokyo, 113–8656 Tokyo, Japan. E-mail: aurelien.cassagnes@gmail.com

Copyright © 2014 John Wiley & Sons, Ltd.

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT

Intell. Sys. Acc. Fin. Mgmt. 21,91–104 (2014)

Published online 6 January 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/isaf.1349