PDTM approach to solve Black Scholes equation for powered ML-Payoff function

Document Type : Research Paper


Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India.


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,$\max\{S^k\ln\big(\frac{S}{K}\big),0\}$ and $\max\{S^k\ln\big(\frac{K}{S}\big),0\}‎, ‎(k\in \mathbb{R^{+}}\cup \{0\})$‎. It is the generalization of Black Scholes model for ML-Payoff functions. It can be seen that values from PDTM are quite accurate to the closed form solutions.


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