A compact finite difference scheme for fractional Black-Scholes option pricing model

Abstract

In this paper, we present a numerical technique for solving the time-fractional Black-Scholes (TFBS) equation describing European options. The time-fractional derivative is described by means of Caputo and a compact finite difference method is employed for discretization of space derivative. Stability and convergence of the fully discrete scheme are studied. Two test problems with the known analytical solutions are considered to demonstrate the efficiency and accuracy of the method and validate the theoretical result. Further, in order to demonstrate the practicability of the method, the method is applied to three European options pricing problems governed by the TFBS equations, where analytical solutions to these problems are not known. We study the effect of fractional order derivative on the solution profile corresponding to option price.