A Tree Model for Pricing Convertible Bonds with Equity, Market and Default Risk

This article presents a trinomial tree model for pricing zero-coupon convertible bonds (CBs) subject to equity, market and default risk. Interest rates are assumed to follow a mean-reverting square root process. Equity prices prior to default are modeled as a constant elasticity of variance (CEV) process, which is capable of reproducing the volatility smile observed in the empirical data. Based on the empirical results, the default intensity is specified as a function of the stock price and interest rate. Embedded call and put options as well as the correlation between interest rates and equity prices are also considered. A numerical example shows the use of the model and numerical results explain the impact of different parameters on the prices of CBs.