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.
| Published in |
Applied and Computational Mathematics (Volume 3, Issue 6-1)
This article belongs to the Special Issue Computational Finance |
| DOI | 10.11648/j.acm.s.2014030601.11 |
| Page(s) | 1-7 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2014. Published by Science Publishing Group |
Analytic Solution, Asian Option, Black-Scholes Model, Mellin Transform Method, Partial Differential Equation
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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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Download@article{10.11648/j.acm.s.2014030601.11,
author = {Fadugba Sunday Emmanuel},
title = {The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option},
journal = {Applied and Computational Mathematics},
volume = {3},
number = {6-1},
pages = {1-7},
doi = {10.11648/j.acm.s.2014030601.11},
url = {https://doi.org/10.11648/j.acm.s.2014030601.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2014030601.11},
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.},
year = {2014}
}
TY - JOUR T1 - The Mellin Transform Method as an Alternative Analytic Solution for the Valuation of Geometric Asian Option AU - Fadugba Sunday Emmanuel Y1 - 2014/08/05 PY - 2014 N1 - https://doi.org/10.11648/j.acm.s.2014030601.11 DO - 10.11648/j.acm.s.2014030601.11 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 1 EP - 7 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.s.2014030601.11 AB - 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. VL - 3 IS - 6-1 ER -
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