IJPAM: Volume 97, No. 3 (2014)

MELLIN TRANSFORM METHOD FOR SOLVING
THE BLACK-SCHOLES EQUATION

F. AlAzemi$^1$, A. AlAzemi$^2$, L. Boyadjiev$^3$
$^{1,2,3}$Department of Mathematics
Faculty of Science
Kuwait Universiry
P.O. Box 5969, Safat, 13060, KUWAIT



This paper is dedicated to Prof. Dr. Rudolf Scherer
Karlsruhe Institute of Technology, Germany
on occasion of his 70$^{\text{th}}$ birthday.


Abstract. In this paper, we obtain an analytical solution of the Black-Scholes equation for the European and the American put options by using the Mellin integral transform method. The analytical solution thus obtained of the Black-Scholes equation for the European put option is compared with the existing already numerical solutions. By using a join Mellin-Laplace integral transforms method, a solution of a boundary value problem for a fractional Black-Scholes equation is also derived. For some prescribed values of the parameters, computational values of the analytical results obtained are compared with some known numerical solutions.

Received: April 1, 2014

AMS Subject Classification: 62P05, 97M30, 91G60, 44A05

Key Words and Phrases: Black-Scholes equation, Mellin integral transform, European put option, American put option, option pricing

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DOI: 10.12732/ijpam.v97i3.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 3
Pages: 287 - 301


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).