Journal of Applied Mathematics
Volume 2 (2002), Issue 5, Pages 219-232
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 R. Mallier and A. S. Deakin. 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.
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.