Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasiček-model is applied to incorporate interest rate risk into the firm's value process which follows a geometric Brownian motion. Finally, we derive pricing bounds for convertible bonds in an uncertain volatility model, i.e. when the volatility of the firm value process lies between two extreme values.
Convertible bond game option uncertain volatility interest rate risk