Within a default intensity approach we discuss the optimal exercise of the callable and convertible bonds. Pricing bounds for convertible bonds are derived in an uncertain volatility model, i.e. when the volatility of the stock price process lies between two extreme values.

Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasiĕk-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...