Improved radial basis function methods for multi-dimensional option pricing

Authors:
Ulrika Pettersson;Elisabeth Larsson;Gunnar Marcusson;Jonas Persson
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;Försäkringsmatematik, Box 5148, SE-102 43 Stockholm, Sweden;SunGard Front Arena, Box 70351, SE-107 24 Stockholm, Sweden
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 7
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Abstract

In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black-Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is second-order accurate in time and spectrally accurate in space for constant shape parameter. For other non-optimal choices of shape parameter values, the resulting convergence rate is algebraic. We propose an adapted node point placement that improves the accuracy compared with a uniform distribution. Compared with an adaptive finite difference method, the RBF method is 20-40 times faster in one and two space dimensions and has approximately the same memory requirements.