A Green's function for a convertible bond using the Vasicek model
In this paper, the authors consider a convertible bond, whose value depends on both the price of the underlying stock that is assumed to obey a lognormal random walk with constant volatility, and on the interest rate that is assumed to follow a random walk given by the Vasicek model. Using a Laplace transform in time, and a Mellin transform with respect to the asset price, they derive a Green's function solution for the value of the convertible bond.
scientific article; zbMATH DE number 1821320