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A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field

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  • Zachary Feinstein
  • Andreas Sojmark

Abstract

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.

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  • Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    • Handle: RePEc:arx:papers:1912.08695
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    1. Craig, Ben & von Peter, Goetz, 2014. "Interbank tiering and money center banks," Journal of Financial Intermediation, Elsevier, vol. 23(3), pages 322-347.
    2. Konstantinos Spiliopoulos & Jia Yang, 2019. "Network Effects in Default Clustering for Large Systems," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(6), pages 523-582, November.
    3. Anastasia Borovykh & Andrea Pascucci & Stefano La Rovere, 2018. "Systemic risk in a mean-field model of interbank lending with self-exciting shocks," IISE Transactions, Taylor & Francis Journals, vol. 50(9), pages 806-819, September.
    4. Gerardo Ferrara & Sam Langfield & Zijun Liu & Tomohiro Ota, 2019. "Systemic illiquidity in the interbank network," Quantitative Finance, Taylor & Francis Journals, vol. 19(11), pages 1779-1795, November.
    5. Iacopo Mastromatteo & Elia Zarinelli & Matteo Marsili, 2012. "Reconstruction of financial network for robust estimation of systemic risk," Post-Print hal-00714026, HAL.
    6. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2015. "Large Portfolio Asymptotics For Loss From Default," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 77-114, January.
    7. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
    8. Tathagata Banerjee & Zachary Feinstein, 2018. "Pricing of debt and equity in a financial network with comonotonic endowments," Papers 1810.01372, arXiv.org, revised Sep 2021.
    9. Paolo Barucca & Marco Bardoscia & Fabio Caccioli & Marco D'Errico & Gabriele Visentin & Guido Caldarelli & Stefano Battiston, 2016. "Network Valuation in Financial Systems," Papers 1606.05164, arXiv.org, revised Jun 2020.
    10. Capponi, Agostino & Chen, Peng-Chu, 2015. "Systemic risk mitigation in financial networks," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 152-166.
    11. Helmut Elsinger, 2009. "Financial Networks, Cross Holdings, and Limited Liability," Working Papers 156, Oesterreichische Nationalbank (Austrian Central Bank).
    12. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362, arXiv.org, revised May 2018.
    13. E. Kromer & L. Overbeck & K. Zilch, 2016. "Systemic risk measures on general measurable spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 323-357, October.
    14. Tathagata Banerjee & Alex Bernstein & Zachary Feinstein, 2018. "Dynamic Clearing and Contagion in Financial Networks," Papers 1801.02091, arXiv.org, revised Jun 2024.
    15. Fang Fei & Sun Yiwei & Spiliopoulos Konstantinos, 2017. "On the effect of heterogeneity on flocking behavior and systemic risk," Statistics & Risk Modeling, De Gruyter, vol. 34(3-4), pages 141-155, September.
    16. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    17. Upper, Christian & Worms, Andreas, 2004. "Estimating bilateral exposures in the German interbank market: Is there a danger of contagion?," European Economic Review, Elsevier, vol. 48(4), pages 827-849, August.
    18. Tobias Adrian & Markus K. Brunnermeier, 2016. "CoVaR," American Economic Review, American Economic Association, vol. 106(7), pages 1705-1741, July.
      • Tobias Adrian & Markus K. Brunnermeier, 2008. "CoVaR," Staff Reports 348, Federal Reserve Bank of New York.
      • Tobias Adrian & Markus K. Brunnermeier, 2011. "CoVaR," NBER Working Papers 17454, National Bureau of Economic Research, Inc.
    19. René Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2018. "Systemic Risk and Stochastic Games with Delay," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 366-399, November.
    20. Andrey Itkin & Alexander Lipton, 2017. "Structural default model with mutual obligations," Review of Derivatives Research, Springer, vol. 20(1), pages 15-46, April.
    21. Tomoyuki Ichiba & Michael Ludkovski & Andrey Sarantsev, 2019. "Dynamic contagion in a banking system with births and defaults," Annals of Finance, Springer, vol. 15(4), pages 489-538, December.
    22. Kartik Anand & Ben Craig & Goetz von Peter, 2015. "Filling in the blanks: network structure and interbank contagion," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 625-636, April.
    23. Cont, Rama & Schaanning, Eric, 2019. "Monitoring indirect contagion," Journal of Banking & Finance, Elsevier, vol. 104(C), pages 85-102.
    24. Iacopo Mastromatteo & Elia Zarinelli & Matteo Marsili, 2011. "Reconstruction of financial network for robust estimation of systemic risk," Papers 1109.6210, arXiv.org, revised Feb 2012.
    25. Yann Braouezec & Lakshithe Wagalath, 2019. "Strategic fire-sales and price-mediated contagion in the banking system," Post-Print hal-02107567, HAL.
    26. Braouezec, Yann & Wagalath, Lakshithe, 2019. "Strategic fire-sales and price-mediated contagion in the banking system," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1180-1197.
    27. Glasserman, Paul & Young, H. Peyton, 2015. "How likely is contagion in financial networks?," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 383-399.
    28. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    29. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    30. Fei Fang & Yiwei Sun & Konstantinos Spiliopoulos, 2016. "The effect of heterogeneity on flocking behavior and systemic risk," Papers 1607.08287, arXiv.org, revised Jun 2017.
    31. Zachary Feinstein & Weijie Pang & Birgit Rudloff & Eric Schaanning & Stephan Sturm & Mackenzie Wildman, 2017. "Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities," Working Paper 2017/13, Norges Bank.
    32. Jean-Pierre Fouque & Zhaoyu Zhang, 2018. "Mean Field Game with Delay: A Toy Model," Risks, MDPI, vol. 6(3), pages 1-17, September.
    33. Zachary Feinstein, 2017. "Obligations with Physical Delivery in a Multi-Layered Financial Network," Papers 1702.07936, arXiv.org, revised May 2019.
    34. Alexander Lipton, 2016. "Modern Monetary Circuit Theory, Stability Of Interconnected Banking Network, And Balance Sheet Optimization For Individual Banks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-57, September.
    35. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    36. Isaac M. Sonin & Konstantin Sonin, 2017. "Banks as Tanks: A Continuous-Time Model of Financial Clearing," Papers 1705.05943, arXiv.org, revised Jul 2020.
    37. Zachary Feinstein, 2018. "Capital Regulation under Price Impacts and Dynamic Financial Contagion," Papers 1807.02711, arXiv.org, revised Aug 2019.
    38. Paul Glasserman & Peyton Young, 2015. "Contagion in Financial Networks," Economics Series Working Papers 764, University of Oxford, Department of Economics.
    39. Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, November.
    40. Dariush Khezrimotlagh & Yao Chen, 2018. "The Optimization Approach," International Series in Operations Research & Management Science, in: Decision Making and Performance Evaluation Using Data Envelopment Analysis, chapter 0, pages 107-134, Springer.
    41. Hamed Amini & Andreea Minca, 2016. "Inhomogeneous Financial Networks and Contagious Links," Operations Research, INFORMS, vol. 64(5), pages 1109-1120, October.
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    3. Hong Chen & Tan Wang & David D. Yao, 2021. "Financial Network and Systemic Risk—A Dynamic Model," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2441-2466, August.

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