Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions. Part II. Early-exercise features and GPU implementation

Zhang, B.; Van der Weide, J.A.M.; Oosterlee, C.W.

Efficient pricing of Asian options under Lévy processes based on Fourier cosine expansions. Part II. Early-exercise features and GPU implementation

Report (2012)

Authors

B. Zhang

J.A.M. Van der Weide

C.W. Oosterlee

Faculty

Electrical Engineering, Mathematics and Computer Science

Earlyexercise Asian option; arithmetic average; Fourier cosine expansion; chain rule; ClenshawCurtis quadrature; exponential convergence; graphics processing unit (GPU) computation

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Published Date

31-03-2012

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Source:

Reports of the Department of Applied Mathematical Analysis, 12-03

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In this article, we propose an efficient pricing method for Asian options with early–exercise features. It is based on a two–dimensional integration and a backward recursion of the Fourier coefficients, in which several numerical techniques, like Fourier cosine expansions, Clenshaw–Curtis quadrature and the Fast Fourier transform (FFT) are employed. Rapid convergence of the pricing method is illustrated by an error analysis. Its performance is further demonstrated by various numerical examples, where we also show the power of an implementation on the Graphics Processing Unit (GPU).

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