Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform

Authors:
Elisabeth Larsson;Krister hlander;Andreas Hall
Affiliations:
Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden;Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden;Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi-dimensional option pricing. We derive a general algorithm, including a transformation of the Black-Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes. Furthermore, the gain increases with the number of dimensions.