Pricing convertible bonds with credit risk under CEV process

In order to construct a model to price convertible bonds, a hybrid security with complicated provisions, this study concentrates on the way of depicting the equity and the default process. The Constant Elasticity of Variance model (CEV model) which modifies the assumption of constant volatility to capture the negative relationship between the stock price and the variance is applied. The default process integrates the information from both equity and debt market by setting the default intensity model to endogenize the default process into the pricing model. The tree structure is built by a manner of variable transformation. After considering all information and deciding whether the provisions to be executed on each node, then the value of convertible bond could be calculated in a backward-induction fashion. Two trading convertible bonds are chosen to examine the practicality of this model and the empirical result shows that this model fit the market value well. The sensitivity analysis suggests that the coefficient of leverage effect does affect the value of convertible bond in an inverse direction and other parameters are not significantly sensitive to the value of convertible bond