A local radial basis function method for high-dimensional American option pricing problems

Abstract

In this work, we apply the local Wendland radial basis function (RBF) for solving the time-dependent multi dimensional option pricing nonlinear PDEs. Firstly, cross derivative terms of the PDE are removed with a change of spatial variables based in LDLT factorization of the diffusion matrix. Then, it is discussed that the valuation of a multi-asset option up to 4D can be computed using a modified shape parameter algorithm. In fact, several experiments containing of three and four assets are worked out showing that the results of the presented method are in good agreement with the literature and could be much more accurate once the shape parameter is chosen carefully.