Solutions of a Time Fractional Black-Scholes Equation Under the Constant Elasticity of Variance Process

Abstract

In this paper we consider backward problem and inverse source problem for time-fractional Black-Scholes equation, which arises from pricing double barrier option under the constant elasticity of variance process. Main tools are spectral method and Sturm-Liouville theory. The existence, uniqueness and convergence analysis of analytic solutions of the backward problem and inverse source problem of time-fractional Black-Scholes model are established in terms of Whittaker functions or modified Bessel functions with large variables.