Numerical Simulations for Time-Fractional Black-Scholes Equations

Abstract

This paper implements an efficient numerical algorithm for the time-fractional Black-Scholes model governing European options. The proposed method comprises the Crank-Nicolson approach to discretize the time variable and exponential B-spline approximation for the space variable. The implemented method is unconditionally stable. We present few numerical examples to confirm the theory. Numerical simulations with comparisons exhibit the supremacy of the proposed approach.