The Adomian Decomposition Method for Standard Power Options

Authors

  • Sanjay J. Ghevariya Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat

DOI:

https://doi.org/10.23755/rm.v42i0.783

Keywords:

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

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.

Author Biography

  • Sanjay J. Ghevariya, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat
    • I have qualified National Eligibility Test (NET) with junior research fellowship three times in 2007 and 2008.
    • I have qualified Graduate Aptitude Test in Engineering (GATE) conducted by Indian Institute of Technology with All India Rank 11 in 2007.
    • I got National Board for Higher Mathematics (NBHM) research award in 2007.
    • National Board for Higher Mathematics (NBHM)(funded by Department of Atomic Energy, New Delhi) Regional Library housed in the department. It is one of the eight NBHM Libraries in INDIA. Also department was recognized by Special Assistant Programme (SAP) funded by Univeristy Grants Commission for three phases.

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Published

2022-06-30

Issue

Vol. 42 (2022)

Section

Volume 42-2022

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