A Continuous Time Structural Model for Insolvency, Recovery, and Rollover Risks

We propose a unified structural credit risk model incorporating insolvency, recovery and rollover risks. The firm finances itself mainly by issuing shortand long-term debt. Short-term debt can have either a discrete or a more realistic staggered tenor structure. We show that a unique threshold strategy (i.e., a bank run barrier) exists for short-term creditors to decide when to withdraw their funding, and this strategy is closely related to the solution of a non-standard optimal stopping time problem with control constraints. We decompose the total credit risk into an insolvency component and an illiquidity component based on such an endogenous bank run barrier together with an exogenous insolvency barrier.