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

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.

Electrical Engineering, Mathematics and Computer Science

2012-03-31

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).

early–exercise Asian option; arithmetic average; Fourier cosine expansion; chain rule; Clenshaw–Curtis quadrature; exponential convergence; graphics processing unit (GPU) computation

http://resolver.tudelft.nl/uuid:3aa47d1d-11bf-4bd8-85ae-c05bacfe7c24

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

1389-6520

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

Institutional Repository

report

(c)2012 Zhang, B., Van der Weide, J.A.M., Oosterlee, C.W.