An efficient pricing method for rainbow options based on two-dimensional modified sine–sine series expansions

Abstract

An efficient option pricing method based on the Fourier cosine series expansion was proposed by Fang and Oosterlee [A novel option pricing method based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 (2008), pp. 826–848], and recently it has been used in two-dimensional cases by Ruijter and Oosterlee [Two-dimensional Fourier cosine series expansion method for pricing financial options, SIAM J. Sci. Comput. 34 (2012), pp. B642–B671]. In this paper, we consider a modification of the Fourier sine–sine expansion, whereby in [−1, 1] the sin(π nx) functions are replaced by sin(π(n−)x), n≥1, for pricing rainbow options. Feasible approaches for obtaining the pricing formulae are presented. A numerical comparison and a flexible and general error analysis are considered to prove the effectiveness of the method. Practical applications to basket options and correlation options under different models are also given. They indicate satisfactory convergence and efficiency as expected.

Keywords:

• two-dimensional Fourier expansions
• modified sine–sine expansions
• rainbow options
• correlation options
• GBM model
• SV model

2010 AMS Subject Classifications:

• 65T40
• 42B05
• 60E10
• 62P05

Acknowledgements

The authors acknowledge the University of Macau for providing support through Grant UL020/08-Y5/MAT/JXQ01/FST and MYRG136(Y2-L2)-FST11-DD. The authors are very grateful to the anonymous referees and the editor for their valuable comments and suggestions, which have improved the paper.