Advertisement

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
Article

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 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.

Keywords

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

JEL Classification

G01 G20 G32 G33 

Notes

Acknowledgments

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.

References

  1. 1.
    Adrian, T., Shin, H.S.: Liquidity and financial contagion. Banq. de Fr. Financ. Stab. Rev.: Spec Issue Liq. 11, 1–7 (2008)Google Scholar
  2. 2.
    Adrian, T., Shin, H.S.: Liquidity and leverage. J. Financ. Intermed. 19(3), 418–437 (2010)CrossRefGoogle Scholar
  3. 3.
    Arifovic, J., Jiang, J.H., Xu, Y.: Experimental evidence of bank runs as pure coordination failures. J. Econ. Dyn. Control 37(12), 2446–2465 (2013)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bielecki, T.R., Rutkowski, M.: Credit Risk: Modeling, Valuation and Hedging. Springer, Berlin (2002)Google Scholar
  5. 5.
    Black, F., Cox, J.: Some effects of bond indenture provisions. J. Financ. 31, 351–367 (1976)CrossRefGoogle Scholar
  6. 6.
    Briys, E., de Varenne, F.: Valuing risky fixed rate debt: an extension. J. Financ. Quant. Anal. 32, 239–249 (1997)CrossRefGoogle Scholar
  7. 7.
    Brunnermeier, M.: Deciphering the liquidity and credit crunch 2007–08. J. Econ. Perspect. 23, 77–100 (2009)CrossRefGoogle Scholar
  8. 8.
    Chen, N., Kou, S.: Credit spread, implied volatility, and optimal capital structures with jump risk and endogenous defaults. Math. Financ. 19, 343–378 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Cheng, I.H., Milbradt, K.: The hazards of debt: rollover freezes, incentives, and bailouts. Rev. Financ. Stud. 25(4), 1070–1110 (2012)CrossRefGoogle Scholar
  10. 10.
    Crépey, S., Grbac, Z., Nguyen, H.N.: A multiple-curve HJM model of interbank risk. Math. Financ. Econ. 6(3), 155–190 (2012)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Diamond, D., Dybvig, P.: Bank runs, deposit insurance and liquidity. J. Polit. Econ. 91, 401–419 (1983)CrossRefGoogle Scholar
  12. 12.
    Ericsson, J., Renault, O.: Liquidity and credit risk. J. Financ. 61, 2219–2250 (2006)CrossRefGoogle Scholar
  13. 13.
    Goldstein, I., Pauzner, A.: Demand-deposit contracts and the probability of bank runs. J. Financ. 60, 1293–1327 (2005)CrossRefGoogle Scholar
  14. 14.
    He, Z., Xiong, W.: Rollover risk and credit risk. J. Financ. 67, 391–429 (2012)CrossRefGoogle Scholar
  15. 15.
    He, Z., Xiong, W.: Dynamic debt runs. Rev. Financ. Stud. 25(6), 1799–1843 (2012)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Hilberink, B., Rogers, L.C.G.: Optimal capital structure and endogenous default. Financ. Stoch. 6, 237–263 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Krylov, N.V.: Controlled Diffusion Processes. Springer, Berlin (2008). 2nd printing editionGoogle Scholar
  18. 18.
    Leland, H.E.: Corporate debt value, bond covenants, and optimal capital structure. J. Financ. 49, 1213–1252 (1994)CrossRefGoogle Scholar
  19. 19.
    Leland, H.E.: Agency costs, risk management, and capital structure. J. Financ. 53, 1213–1243 (1998)CrossRefGoogle Scholar
  20. 20.
    Leland, H.E., Toft, K.: Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. J. Financ. 51, 987–1019 (1996)CrossRefGoogle Scholar
  21. 21.
    Liang, G.: Stochastic control representations for penalized backward stochastic differential equations. arXiv:1302.0480 (2013, Preprint)
  22. 22.
    Liang, G., Jiang, L.: A modified structural model for credit risk. IMA J. Manag. Math. 23, 147–170 (2012)CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    Liang, G., Lütkebohmert, E., Xiao, Y.: A multi-period bank run model for liquidity risk. Rev. Financ. 18(2), 803–842 (2014)CrossRefGoogle Scholar
  24. 24.
    Liang, G., Lütkebohmert, E., Wei, W.: A continuous time structural model for insolvency, recovery, and rollover risks. http://ssrn.com/abstract=2147466 (2012, Preprint)
  25. 25.
    Longstaff, F., Schwartz, E.: A simple approach to valuing risky fixed and floating rate debt. J. Financ. 50, 789–819 (1995)CrossRefGoogle Scholar
  26. 26.
    Merton, R.C.: On the pricing of corporate debt: the risk structure of interest rates. J. Financ. 29, 449–470 (1974)Google Scholar
  27. 27.
    Morris, S., Shin, H.S.: Illiquidity component of credit risk. www.banqueducanada.ca/wp-content/uploads/2010/09/Illiquidity-Component (2010, Preprint)
  28. 28.
    Morris, S., Shin, H.S.: Global games: theory and applications. In: Dewatripont, M., Hansen, L., Turnovsky, S. (eds.) Advances in Economics and Econometrics (Proceedings of the Eighth World Congress of the Econometric Society), pp. 56–1154. Cambridge University Press, Cambridge (2003)Google Scholar

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

Personalised recommendations