Perpetual Convertible Bonds

Perpetual Convertible Bonds

A firm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold the bond, thereby collecting coupons, or to convert it to stock. The firm may at any time call the bond. Because calls and conversions often occur far from maturity, it is not unreasonable to model this situation with a perpetual convertible bond, i.e., a convertible coupon-paying b...

Perpetual convertible bonds in jump-diffusion models

A convertible (callable) bond is a security that the holder can convert into a specified number of underlying shares. In addition, the issuer can recall the bond, paying some compensation, or force the holder to convert it immediately. We give an explicit solution to the corresponding optimal stopping game in the context of a reduced form model driven by a Brownian motion and a compound Poisson...

Perpetual convertible bonds with credit risk

A convertible bond is a security that the holder can convert into a specified number of underlying shares. We enrich the standard model by introducing some default risk of the issuer. Once default has occured payments stop immediately. In the context of a reduced form model with infinite time horizon driven by a Brownian motion, analytical formulae for the no-arbitrage price of this American co...

The Valuation of Convertible Bonds

Convertible Bonds with Call Notice Periods

In practice, convertible bonds can often be called only if notice is given to the holders. Most methods for valuing convertible bonds assume that the bond is continuously callable. In this paper, we develop an accurate PDE method for valuing convertible bonds with a finite notice period. Example computations are presented which illustrate the effect of varying notice periods. The results are co...