GPU acceleration of the stochastic grid bundling method for early-exercise options

Abstract

In this work, a parallel graphics processing units (GPU) version of the Monte Carlo stochastic grid bundling method (SGBM) for pricing multi-dimensional early-exercise options is presented. To extend the method's applicability, the problem dimensions and the number of bundles will be increased drastically. This makes SGBM very expensive in terms of computational costs on conventional hardware systems based on central processing units. A parallelization strategy of the method is developed and the general purpose computing on graphics processing units paradigm is used to reduce the execution time. An improved technique for bundling asset paths, which is more efficient on parallel hardware is introduced. Thanks to the performance of the GPU version of SGBM, a general approach for computing the early-exercise policy is proposed. Comparisons between sequential and GPU parallel versions are presented.

Keywords:

• computational finance
• early-exercise derivatives
• basket Bermudan options
• high-dimensional pricing
• stochastic grid bundling method (SGBM)
• Monte Carlosimulation
• least-squares regression
• high performance computing
• parallel programming
• GPGPU
• compute unified device architecture (CUDA)

2010 AMS Subject Classifications:

• 91G60
• 91G70
• 65Y05
• 65C05
• 65C10

Acknowledgments

The authors would like to thank Shashi Jain, ING Bank, for providing support and the original codes of the SGBM.

Thanks to SURFsara for providing the access to Accelerator Island system of the Cartesius Supercomputer to perform our experiments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The first author is supported by the European Union in the FP7-PEOPLE-2012-ITN Program [grant number 304617] (FP7 Marie Curie Action, Project Multi-ITN STRIKE – Novel Methods in Computational Finance).

Notes

1. Double-precision floating-point format.

2. Application programming interface.