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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Ghevariya, S. (2022). PDTM approach to solve Black Scholes equation for powered ML-Payoff function. Computational Methods for Differential Equations, 10(2), 320-326. doi: 10.22034/cmde.2021.37944.1675
MLA
Sanjay J Ghevariya. "PDTM approach to solve Black Scholes equation for powered ML-Payoff function". Computational Methods for Differential Equations, 10, 2, 2022, 320-326. doi: 10.22034/cmde.2021.37944.1675
HARVARD
Ghevariya, S. (2022). 'PDTM approach to solve Black Scholes equation for powered ML-Payoff function', Computational Methods for Differential Equations, 10(2), pp. 320-326. doi: 10.22034/cmde.2021.37944.1675
VANCOUVER
Ghevariya, S. PDTM approach to solve Black Scholes equation for powered ML-Payoff function. Computational Methods for Differential Equations, 2022; 10(2): 320-326. doi: 10.22034/cmde.2021.37944.1675
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