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.
کلید واژگان :
Option pricing Black–Scholes American option European option Meshless weak form Moving least squares
