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. © 2007 Elsevier B.V. All rights reserved.
Pettersson, U., Larsson, E., Marcusson, G., & Persson, J. (2008). Improved radial basis function methods for multi-dimensional option pricing. Journal of Computational and Applied Mathematics, 222(1), 82–93. https://doi.org/10.1016/j.cam.2007.10.038