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Credit Risk in a Network Economy

Author

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  • Didier Cossin

    (IMD, CH-1001 Lausanne, Switzerland)

  • Henry Schellhorn

    (School of Mathematical Sciences, Claremont Graduate University, Claremont, California 91711)

Abstract

We develop a structural model of credit risk in a network economy, where any firm can lend to any other firm, so that each firm is subject to counterparty risk either from direct borrowers or from remote firms in the network. This model takes into account the role of each firm's cash management. We show that we can obtain a semiclosed form formula for the price of debt and equity when cash accounts are buffers to bankruptcy risk. As in other structural models, the strategic bankruptcy decision of shareholders drives credit spreads, and differentiates debt from equity. Cash-flow risk also causes credit-risk interdependencies between firms. Our model applies to the case where not only financial flows but also operations are dependent across firms. We use queueing theory to obtain our semiclosed form formulae in steady state. We perform a simplified implementation of our model to the U.S. automotive industry, and show how we infer the impact on a supplier's credit spreads of revenue changes in a manufacturer or even in a large car dealer. We also obtain prices for first-to-default and second-to-default basket credit default swaps.

Suggested Citation

  • Didier Cossin & Henry Schellhorn, 2007. "Credit Risk in a Network Economy," Management Science, INFORMS, vol. 53(10), pages 1604-1617, October.
  • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:10:p:1604-1617
    DOI: 10.1287/mnsc.1070.0715
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    References listed on IDEAS

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    2. Wenlang Zhang & Gaofeng Han & Steven Chan, 2014. "How Strong are the Linkages between Real Estate and Other Sectors in China?," Working Papers 112014, Hong Kong Institute for Monetary Research.
    3. Mizgier, Kamil J. & Wagner, Stephan M. & Jüttner, Matthias P., 2015. "Disentangling diversification in supply chain networks," International Journal of Production Economics, Elsevier, vol. 162(C), pages 115-124.
    4. Vandana, & Kaur, Arshinder, 2019. "Two-level trade credit with default risk in the supply chain under stochastic demand," Omega, Elsevier, vol. 88(C), pages 4-23.
    5. Ladley, Daniel, 2013. "Contagion and risk-sharing on the inter-bank market," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1384-1400.
    6. Raffaella Calabrese & Galina Andreeva & Jake Ansell, 2019. "“Birds of a Feather” Fail Together: Exploring the Nature of Dependency in SME Defaults," Risk Analysis, John Wiley & Sons, vol. 39(1), pages 71-84, January.
    7. Tingqiang Chen & Xindan Li & Jining Wang, 2015. "Spatial Interaction Model of Credit Risk Contagion in the CRT Market," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 519-537, December.
    8. Paolo Barucca & Marco Bardoscia & Fabio Caccioli & Marco D'Errico & Gabriele Visentin & Guido Caldarelli & Stefano Battiston, 2020. "Network valuation in financial systems," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1181-1204, October.
    9. Spiros Bougheas & Alan Kirman, 2015. "Complex Financial Networks and Systemic Risk: A Review," Dynamic Modeling and Econometrics in Economics and Finance, in: Pasquale Commendatore & Saime Kayam & Ingrid Kubin (ed.), Complexity and Geographical Economics, edition 127, pages 115-139, Springer.
    10. Leonidas Sandoval Junior, 2014. "Dynamics in two networks based on stocks of the US stock market," Papers 1408.1728, arXiv.org, revised Aug 2014.
    11. Sandoval, Leonidas Junior, 2013. "To lag or not to lag? How to compare indices of stock markets that operate at different times," Insper Working Papers wpe_319, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    12. Fanelli, Viviana & Maddalena, Lucia, 2020. "A nonlinear dynamic model for credit risk contagion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 45-58.
    13. Barro, Diana & Basso, Antonella, 2010. "Credit contagion in a network of firms with spatial interaction," European Journal of Operational Research, Elsevier, vol. 205(2), pages 459-468, September.
    14. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    15. Chan, Steven & Han, Gaofeng & Zhang, Wenlang, 2016. "How strong are the linkages between real estate and other sectors in China?," Research in International Business and Finance, Elsevier, vol. 36(C), pages 52-72.
    16. Jian Yang & Yinggang Zhou, 2013. "Credit Risk Spillovers Among Financial Institutions Around the Global Credit Crisis: Firm-Level Evidence," Management Science, INFORMS, vol. 59(10), pages 2343-2359, October.
    17. Eriksson, Kent & Jonsson, Sara & Lindbergh, Jessica & Lindstrand, Angelika, 2014. "Modeling firm specific internationalization risk: An application to banks’ risk assessment in lending to firms that do international business," International Business Review, Elsevier, vol. 23(6), pages 1074-1085.
    18. Hofmann, Erik, 2011. "Risk management in international supply chains: the case of natural hedging," Die Unternehmung - Swiss Journal of Business Research and Practice, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 65(2), pages 155-192.
    19. Sui, Xin & Li, Liang & Chen, Xiaohui, 2020. "Risk contagion caused by interactions between credit and guarantee networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    20. Shulin Zhang, & Ostap Okhrin, & Qian M. Zhou & Peter X.-K. Song, 2013. "Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models," SFB 649 Discussion Papers SFB649DP2013-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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