In this paper, a new method called partial Taylor series expansion method is applied to Black–Scholes differential equation for Log-Payoff function. The analytical method was used to develop solutions for the call and put options pricing for the classical Black–Scholes equations for the Log Payoff functions. The new method displayed high level of simplicity and low cost of computation. Moreover, the reliability, speed, accuracy, and ease of application of the proposed method show its potential for wide areas of applications in science, financial mathematics, and engineering.
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