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Abstract and Applied Analysis
Volume 2014, Article ID 709871, 10 pages
http://dx.doi.org/10.1155/2014/709871
Research Article

Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

1International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
2Department of Mathematics and Computer Science, University of Lesotho, Roma 180, Lesotho

Received 30 January 2014; Accepted 24 March 2014; Published 13 April 2014

Academic Editor: Imran Naeem

Copyright © 2014 Tanki Motsepa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.