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Abstract
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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
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