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

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

R. Mallier and A. S. Deakin

 Department of Applied Mathematics, The University of Western Ontario, London N6A 5B7, Ontario, Canada
Received 13 March 2002

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.