Pricing a Convert Bond with Default Risk under a Reduced Form Model

In this study, we consider the pricing problem of convert bond with default risk under a reduced form model. We suppose that the default intensity follows the Vasicek model, and obtain a closed form pricing formula of convert bond by martingale method. Moreover, we provide a numerical analysis to demonstrate the sensitivity of a default convert bond value to changes in the model's parameters, and show that the default risk of convert bond issuer will reduce the convert bond value.