Optimal stopping framework for valuing convertible bonds with intensity to model uncertain call notice

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Empirical research shows that the call provision embedded in the convertible bonds and American call options may be delayed for different reasons. While there are several researches focused on recall provision embedded in the callable American call options under intensity-based framework, few performed detailed research on that in convertible bonds. Therefore, the main purpose of the current work is to model and study the call provision embedded in the callable convertible bonds using intensity-based approach. We formulate this as an optimal stopping problem. Under certain assumptions, we can then get a nonlinear complementarity problem that can be solved by numerical procedures. We also consider credit risk. Since there are already lots of literatures on this, we only provide a theoretical formulation under the AFV model framework.