Pricing Convertible Bonds by Simulation

Convertible bonds are complex hybrid securities subject to multiple sources of risk. Many exhibit exotic path dependent features. Monte Carlo method is usually the favorite choice for solving high-dimensional problems and pricing path dependent securities. This paper breaks away from the tradition established in the literature of pricing convertible bonds with finite difference and lattice methods, and suggests a simulation methodology for convertible bond pricing. We introduce the dividend process for convertible bonds, and formulate the pricing problem according to the probabilistic martingale approach. The proposed methodology deals with convertible bonds, subject to credit risk, with call and put features. The early exercise rules are estimated by means of least squares regressions as in Longstaff and Schwartz (2001). The accuracy of the simulation algorithm is tested in the context of a two factor model. The algorithm performs fairly well, and shows potential for further extension to include many complexities inherent in convertible bonds, as well as additional risk factors.