A numerical study of RBFs-DQ method for multi-asset option pricing problems

Abstract

In this paper, we propose a numerical scheme to solve multi-dimensional Black-Scholes equation using the global radial basis functions-based differential quadrature (RBFs-DQ) method. Before applying the method, it is needed to remove mixed derivatives from the Black-Scholes equation by making an appropriate change of variables. Then, any spatial derivativeis are approximated by a linear weighted sum of all the function values in the whole physical domain. In the RBFs-DQ method the weighting coefficients are computed by RBFs. The method is very easy to implement and the non-singularity is ensured. The proposed method combines the advantages of the conventional DQ method and the RBFs. It also preserves mesh-free feature of RBFs.