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Journal of Applied Mathematics
Volume 2 (2002), Issue 5, Pages 219-232
http://dx.doi.org/10.1155/S1110757X02203058

A Green′s function for a convertible bond using the Vasicek model

Department of Applied Mathematics, The University of Western Ontario, London N6A 5B7, Ontario, Canada

Received 13 March 2002

Copyright © 2002 Hindawi Publishing Corporation. 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 consider a convertible security where the underlying stock price obeys a lognormal random walk and the risk-free rate is given by the Vasicek model. Using a Laplace transform in time and a Mellin transform in the stock price, we derive a Green′s function solution for the value of the convertible bond.