THE CRANK NICOLSON METHOD COUPLED WITH PROJECTED SUCCESSIVE OVER RELAXATION IN VALUING STANDARD OPTION WITH DIVIDEND PAYING STOCK

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Published: Jul 26, 2015

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Gabriel Obed Fosu
Presbyterian University College, Abetifi, Ghana
Awudu Obeng
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Francis T Oduro
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Gabriel A Okyere
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

Abstract

We review options pricing with dividend paying stock on a single asset. We start from the Black-Scholes
equation with a free boundary value, the free boundary value problem is then transformed into a Linear Complementarity
Problem, and an Obstacle Problem. We solve the Linear Complementarity Problem by introducing the method of Finite
Difference method - Crank-Nicolson scheme. This leads to a constraint linear system of equations which is solved on a
discrete domain by applying the Projected Successive Over Relaxation (PSOR) method. The simulation results showed
that the price of the American option exceeds the analytical solution. The payoff function intersects the European option
at lower prices relative to the American option; this gives us the early exercise value. We conclude that the American
option with dividend paying stock is preferred to the European option.

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How to Cite
Fosu, G. O., Obeng, A., Oduro, F. T., & Okyere, G. A. (2015). THE CRANK NICOLSON METHOD COUPLED WITH PROJECTED SUCCESSIVE OVER RELAXATION IN VALUING STANDARD OPTION WITH DIVIDEND PAYING STOCK. Journal of Global Research in Mathematical Archives(JGRMA), 2(9), 01–15. Retrieved from https://www.jgrma.com/index.php/jgrma/article/view/251
Issue
Vol. 2 No. 9 (2014): September-2014
Section
Research Paper

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