A Radial Basis Function Method for Solving Options Pricing Model

This paper applies the global radial basis functions as a spatial collocation scheme for solving the Options Pricing model. Diierent numerical time integration schemes are employed for the time derivative of the model. In the case of the European options, it is shown that the major numerical error is from the time integration instead of the spatial approximation by comparing with the analytical solution. The numerical results for the American options indicate that this proposed scheme ooers a highly accurate approximation compared with existing numerical methods. Since the basis functions are innnitely diierentiable, the numerical approximation of the derivatives of the options price can be computed directly without using extra interpolation techniques. The numerical approximation of the optimal exercise boundary in the case of American options can also be obtained eeectively by using the Newton's iterative scheme.