Analytical Solution of the Time-fractional Order Black-Scholes Model for Stock Option Valuation on No Dividend Yield Basis.

In this work, we obtain analytical solutions of the time-fractional Black-Scholes equation for European call option via a proposed relatively new semi-analytic technique hereby referred to as Projected Differential Transform Method (PDTM). This algorithmic technique is a modified version of the classical Differential Transformation Method (DTM). We demonstrate the efficiency and accuracy of the proposed technique by solving some illustrative problems. The results are obtained with ease and less computational work. No linearization or perturbation is required unlike other contemporary techniques. Thus, our results show that the work of Edeki et al. [42] is a particular case of this present work. This proposed technique is being reported for the first time in literature for solving time-fractional Black-Scholes equation. It is therefore recommended as an alternative technique for solving linear and nonlinear equations resulting from timefractional stochastic differential equations (TFSDEs) in financial mathematics, with particular attention to stock option valuation; and fractional equations in applied sciences. [ABSTRACT FROM AUTHOR]