Journal of Applied Mathematics
Volume 2010 (2010), Article ID 263451, 5 pages
doi:10.1155/2010/263451
Research Article

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

A. S. Deakin1 and Matt Davison1,2

1Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada
2Department of Statistical & Actuarial Sciences, University of Western Ontario, London, ON, N6A 5B7, Canada

Received 31 May 2009; Revised 5 November 2009; Accepted 6 January 2010

Academic Editor: Peter Spreij

Copyright © 2010 A. S. Deakin and Matt Davison. 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

This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.