DELFT UNIVERSITY OF TECHNOLOGY REPORT 11-11 Efficient Pricing of Asian Options under Lévy Processes based on Fourier Cosine Expansions Part I: European-Style Products

We propose an efficient pricing method for arithmetic, and geometric, Asian options under Lévy processes, based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European–style and American–style Asian options, and for discretely and continuously monitored versions. In the present paper we focus on European–style Asian options; American-style options are treated in an accompanying part II of this paper. The exponential convergence rate of Fourier cosine expansions and Clenshaw–Curtis quadrature reduces the CPU time of the method to milli-seconds for geometric Asian options and a few seconds for arithmetic Asian options. The method’s accuracy is illustrated by a detailed error analysis, and by various numerical examples.