A NEW FINITE DIFFERENCE/SPECTRAL METHOD FOR NUMERICAL SOLUTION OF THE BLACK–SCHOLES EQUATION FOR EUROPEAN PUT OPTIONS

The main purpose of this paper is to investigate a new numerical method based on backward finite difference method and spectral Galerkin method for solving Black–Scholes equation for European put option. In this paper, by discretization in time for the Black-scholes equation we get the ordinary system of differential equations (ODEs) in the spatial domain. The obtained ODEs is solved by applying the spectral Galerkin method based on the generalized Jacobi polynomials. The convergence of the method in suitable spaces of functions, equipped with the weighted L 2 - norm is discussed. Also, we provide numerical experiment to show the accuracy of method.