Analytical Solutions of Time Space Fractional Black-Scholes Option Pricing Model with Their Applications

In recent years fractional partial differential equations and their solutions through analytical methods is a dynamic and imperative research area. In this context finding the exact solution of fractional partial differential equations by employing variant tactics has been the pivotal region of working since the beginning. In this paper , the analytical solutions of time space fractional Black-Scholes model using the new Sumudu transform iterative method (NSTIM) with the aid of fractional complex transform (FCT) are presented. We deal with the time fractional derivative of order 0 < γ ≤ 1 and space fractional derivative of order 0 < 2λ ≤ 2. We review the particular cases of time space derivatives in each case for γ = λ = 1. Proposed method proves to be very effective with easily computed results. Numerical results are in complete agreement with the application of this method in solving various linear and non-linear fractional differential equations (FDEs) in terms of stochastic dynamics in financial mathematics