Mathematics and Financial Economics

, Volume 9, Issue 4, pp 271–302 | Cite as

Funding liquidity, debt tenor structure, and creditor’s belief: an exogenous dynamic debt run model

  • Gechun LiangEmail author
  • Eva Lütkebohmert
  • Wei Wei


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 mainly 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.


Structural credit risk model Debt run Liquidity risk First passage time Optimal stopping time 

JEL Classification

G01 G20 G32 G33 



The article was previously circulated under the title A Continuous Time Structural Model for Insolvency, Recovery, and Rollover Risks [24]. We thank the Editor-in-Chief, Ulrich Horst, a Co-Editor, an Associate Editor, and a Referee for their valuable comments and suggestions. Several helpful comments and suggestions from Lishang Jiang, Yajun Xiao, and Qianzi Zeng are very much appreciated. We also thank the participants at the Conference on Liquidity and Credit Risk in Freiburg 2012, the INFORMS International Meeting in Beijing 2012, the 4th Berlin Workshop on Mathematical Finance for Young Researchers in Berlin 2012, the 2013 International Conference on Financial Engineering, in Suzhou 2013, the 6th Financial Risks International Forum on Liquidity Risk in Paris 2013, the IMA Conference on Mathematics in Finance in Edinburgh 2013, the 30th French Finance Association Conference in Lyon 2013, and the European Financial Management Association 2013 Annual Meetings in Reading 2013, as well as seminar participants at the University of Oxford, Imperial College, University of Texas at Austin, and Tongji University for several insightful remarks. The work was supported by the Oxford-Man Institute of Quantitative Finance, University of Oxford, by the Excellence Initiative through the project Pricing of Risk in Incomplete Markets within the Institutional Strategy of the University of Freiburg as well as by the German Research Foundation through the project Modelling of Market, Credit and Liquidity Risks in Fixed-Income Markets.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsKing’s College LondonLondonUK
  2. 2.Department of Quantitative FinanceUniversity of FreiburgFreiburgGermany
  3. 3.Mathematical InstituteUniversity of OxfordOxfordUK

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