RBF Based Multilevel Meshfree Approximation in Model Including Market Illiquidity

This paper addresses application of multilevel Newton iteration along with the radial basis functions to be used for solving the parabolic partial differential equations derived from pricing European options in the Frey and Patie model. The linearization of the nonlinear PDE applied at each iteration helps to solve a system of linear PDEs by a multilevel collocation scheme. Finally, in order to evaluate the accuracy and robustness of the results gained in this paper, they are compared with the results from former numerical studies.