The Valuation of Convertible Bonds: A Study of Alternative Pricing

Convertible debt represents 10% of all USA debt yet despite its ubiquity it still posses difficult modelling challenges. This paper investigates alternative convertible bond model specifications. The work reviews the literature on convertible debt valuation especially the methodologies adopted by practitioners. Inadequacies in the historical and current valuation methods are highlighted. The different features used in convertible bond contracts found on the International Security Markets Association database are catalogued for both the Japanese and USA markets. Fashions in the contracts that have changed through time are noted. Modal, average, maximum and minimum USA contract parameters for various features are used to establish realistic and representative convertible bond contracts. The motivation for analyzing the ISMA data is determine which contracts features are important before investigating model errors. The model errors themselves are a function of the contract in question and cannot therefore, be examined in abstract. The sensitivity of the modal convertible bond contract price to the method of modelling the spot interest rate and the intensity process is examined. The convertible bond price sensitivity to the input parameters reveals that accurately modelling the equity process and capturing the contract clauses in the numerical approximation appear crucial whereas the intensity rate and spot interest rate processes are of second order importance.