Multidimensional Shannon Wavelet Inverse Fourier Technique for Pricing Financial European Options

Abstract

The SWIFT method for pricing European options with one underlying asset was developed in L. Ortiz-Gracia and C. W. Oosterlee. A highly effcient Shannon wavelet inverse Fourier technique for pricing European options. SIAM J. Sci. Comput., 38(1):B18-B143, 2016, presented as an accurate, robust and highly efficient technique. The purpose of this paper is to extend the method to higher dimensions by pricing exotic option contracts, called rainbow options, whose payoff depends on multiple assets. The multidimensional extension inherits the properties of the one-dimensional method, being the exponential convergence one of them. Thanks to the nature of local Shannon wavelets basis, we do not need to rely on a-priori truncation of the integration range, we have an error bound estimate and we use fast Fourier transform (FFT) algorithms to speed up computations. We test the method for similar examples as the ones used with the 2D-COS method presented in M. J. Ruiter and C. W. Oosterlee. Two-dimensional Fourier cosine series expansion method for pricing financial options. SIAM J. on Scientific Computing, 34(5):B642-B671, 2012, and we compare our results with analytical expressions when available.