### The Adomian Decomposition Method for Standard Power Options

Sanjay J. Ghevariya

#### Abstract

Black-Scholes model derived by Black and Scholes is worldwide used mathematical model for valuing option price. This model brings a new quantitative approach for researcher to finding theoretical values of options. They derived the model of European options for plain vanilla payoffs. Black-Scholes model derived from Black-Scholes differential equation which is parabolic in nature. In this paper, a well-known accurate, simple, semi-analytical method, the Adomian decomposition method (ADM), is used for Black-Scholes differential equation for standard power payoffs. This model is the generalization of plain vanilla payoffs. Further, it can be seen that the cumulative distribution function of standard normal random variable is used in the closed form formulas of standard power options, while our formulas do not involve any term regarding random variable. In fact our formulas are impressive, fruitful and very close to the closed form formulas. Numerical results shows that our approach gives very accurate results.

#### Keywords

Black-Scholes theory; Adomian Decomposition Method; Standard Power Options.

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DOI: http://dx.doi.org/10.23755/rm.v42i0.783

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