A tree model for pricing convertible bonds with equity, interest rate, and default risk

This article presents a binomial tree model for pricing convertible bonds. Our model is a two-factor model (interest rates and equity prices) in which the potential for default is modeled in the manner of Jarrow and Turnbull [1995]. Interest rates are modeled using the Ho-Lee [1986] lognormal model. Equity prices are modeled using the Cox-Ross-Rubinstein (CRR) model. Our model differs from Das and Sundaram [2006] through differences in the specification of the correlation between interest rates and stock prices. Our model also differs from the model of Hung and Wang [2002] who, among other differences, assume no correlation. We model correlation analogously to the approach of Hull [2003, p. 474]. We demonstrate the simplicity of our model and compare the pricing of our model with the pricing of Hung and Wang using. the numerical examples from their article. We find moderate pricing differences between the models and provide sensitivity analysis of the effect of correlation between the interest rate and equity factors.