Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Abstract

In this paper, a method for the numerical pricing of American and European options under the Black–Scholes model is introduced. This approach is meshless local Petrov–Galerkin (MLPG) based on local weak form and the moving least squares approximations. The MLPG offers advantages over conventional and strong meshless methods of radial basis function approximations. In this paper, the American option which is a free boundary problem, is reduced to a fixed boundary problem using a Richardson extrapolation technique. Then a time stepping method is employed for the time derivative. Finally numerical results are presented in two test cases. These experiments show that MLPG approach is accurate and fast, and performs significantly better compared to the conventional radial basis functions collocation methods.