Open this publication in new window or tab >>2006 (English)Report (Other academic)
Abstract [en]
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 adaptive 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.
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2006-028
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-80801 (URN)
2008-02-132008-02-132024-05-31Bibliographically approved