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Abstract
We propose a unified structural credit risk model incorporating both insolvency and
illiquidity risks, in order to investigate how a firm's default probability depends
on the liquidity risk associated with its financing structure. We assume the firm
finances its risky assets by issuing short- and long-term debt. Short-term debt can
have either a discrete or a more realistic staggered tenor structure. At rollover
dates of short-term debt, creditors face a dynamic coordination problem. We show that
a unique threshold strategy (i.e., a debt 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 debt run barrier together with an exogenous
insolvency barrier.
Comments 40 pages, 9 figures, 4 tables. The article was previously circulated
under the title A Continuous Time Structural Model for Insolvency, Recovery,
and Rollover Risks