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

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),۰\} and \max\{S^k\ln\big(\frac{K}{S}\big),۰\}‎, ‎(k\in \mathbb{R^{+}}\cup \{۰\})‎. 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.

کلیدواژه ها:

Black Scholes formulas ، Projected Differential Transform Method ، ML-Payoff functions ، plain vanilla options