ON THE GEGENBAUR PSEUDOSPECTRAL METHOD FOR THE TIME FRACTIONAL BLACK-SCHOLES EUROPEAN OPTION PRICING MODEL

Abstract. The time fractional Black–Scholes model(TFBSM) is employed to price American or European call and put options on a stock paying on a non-dividend basis. In this paper, We examine pseudospectral method for numerical solution of TFBSM, based on Gegenbauer polynomials and Chebyshev spectral differentiation matrix . The presented method reduces TFBSM to a generalized Sylvester matrix equation, which can be solved by the global GMRES method.