PDTM Approach to Solve Black Scholes Equation for Powered ML-Payoff Function

Abstract

In this paper, the Projected Differential Transform Method (PDTM) has been used to solve the Black Scholes differential equation for powered Modified Log Payoff (ML-Payoff) functions, $max {S^klnbig(frac{S}{K}big),0}$ and $max{S^klnbig(frac{K}{S}big),0}, (kin mathbb{R^{+}}cup {0})$. It is the generalization of Black Scholes model for ML-Payoff functions. It can be seen that values from PDTM is quite accurate to the closed form solutions.