(A) study on perpetual convertible bond

Abstract

A convertible bond is issued by a firm. At each instant in time, the bondholder must decide whether to continue to hold the bond, or to convert it to stock. The firm may call the bond at any time. Because calls and conversions often occur far from maturity, it is not unreasonable to model this situation with a perpetual convertible bond. This model admits a relatively simple solution, under which the value of the perpetual convertible bond, as a function of the value of the underlying firm, is determined by a ordinary differential equation. In case of stochastic interest rate model, the value function is determined by a partial differential equation.