Binary Tree Pricing to Convertible Bonds with Credit Risk under Stochastic Interest Rates

The convertible bonds usually have multiple additional provisions that make their pricing problem more difficult than straight bonds and options. This paper uses the binary tree method to model the finance market. As the underlying stock prices and the interest rates are important to the convertible bonds, we describe their dynamic processes by different binary tree. Moreover, we consider the influence of the credit risks on the convertible bonds that is described by the default rate and the recovery rate; then the two-factor binary tree model involving the credit risk is established. On the basis of the theoretical analysis, we make numerical simulation and get the pricing results when the stock prices are CRR model and the interest rates follow the constant volatility and the time-varying volatility, respectively. This model can be extended to other financial derivative instruments