A Binomial-Tree Model for Convertible Bond Pricing

In this article, we derive a binary tree–based model for convertible bond valuation subject to credit risk modeling. Our model, which belongs to the framework known as equity to credit risk, is based on the so-called reduced-form (constant intensity of default model for the underlying) and so-called synthesis (variable intensity of default model for the underlying) credit risk models. We show that our model converges in continuous time to the Ayache–Forsyth–Vetzal convertible bond valuation model introduced in 2003. We highlight and quantify certain issues that arise, such as transition probability analysis and threshold values of model inputs (tree step and underlying stock price). The model we propose provides an alternative way to develop the price dynamics model suggested by the Ayache–Forsyth–Vetzal model for convertible bonds, taking into account credit risk. TOPICS:Fixed income and structured finance, fixed-income portfolio management, options, factor-based models