Application of Space-Time Localized Radial Basis Functions Scheme to Solve the American and European Options Pricing Models

In this paper, we investigate the use of space-time localized radial basis function collocation method to solve the options pricing European and American models. The application of the proposed method to options pricing European and American models open a new area in the development of this technique for solving partial differential equations (PDEs) with variable coefficients. Beside the known advantages of the method when solving the PDEs with constant coefficients, re-computing the resulting matrix and solving the algebraic system at each time level, as done by time stepping method when solving PDEs with variable coefficients, are avoided. In herein, the numerical approximation of the optimal exercise boundary in the case of American options is obtained effectively by using a new algorithm of penalty iterative scheme. The same technique is applied to the two and three-dimensional American options without boundary conditions when considering the problem in the space domain. Results are compared with analytical and available published numerical results. Obtained results indicate that the proposed scheme offers accurate approximation compared with existing numerical methods applied to such option pricing European and American models.