### The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option

Received: 19 July 2014    Accepted: 5 August 2014    Published: 5 August 2014

Abstract

This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this is due to the fact that the geometric average of a set of lognormal random variables is lognormally distributed. We derive a closed form solution for a continuous geometric Asian option by means of the partial differential equations. We also provide an alternative method for solving geometric Asian options partial differential equations using the Mellin transform method.

Keywords

Analytic Solution, Asian Option, Black-Scholes Model, Mellin Transform Method, Partial Differential Equation

References
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• APA Style

Fadugba Sunday Emmanuel. (2014). The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option. Applied and Computational Mathematics, 3(6-1), 1-7. https://doi.org/10.11648/j.acm.s.2014030601.11

ACS Style

Fadugba Sunday Emmanuel. The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option. Appl. Comput. Math. 2014, 3(6-1), 1-7. doi: 10.11648/j.acm.s.2014030601.11

AMA Style

Fadugba Sunday Emmanuel. The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option. Appl Comput Math. 2014;3(6-1):1-7. doi: 10.11648/j.acm.s.2014030601.11

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abstract = {This paper presents the Mellin transform method as an alternative analytic solution for the valuation of geometric Asian option. Asian options are options in which the variable is the average price over a period of time. The analytical solution of the Black-Scholes partial differential equation for Asian option is known as an explicit formula, this is due to the fact that the geometric average of a set of lognormal random variables is lognormally distributed. We derive a closed form solution for a continuous geometric Asian option by means of the partial differential equations. We also provide an alternative method for solving geometric Asian options partial differential equations using the Mellin transform method.},
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Author Information
• Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria

• Sections