IDEAS home Printed from https://ideas.repec.org/a/kap/annfin/v15y2019i4d10.1007_s10436-019-00351-2.html
   My bibliography  Save this article

Dynamic contagion in a banking system with births and defaults

Author

Listed:
  • Tomoyuki Ichiba

    (University of California)

  • Michael Ludkovski

    (University of California)

  • Andrey Sarantsev

    (University of Nevada)

Abstract

We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:annfin:v:15:y:2019:i:4:d:10.1007_s10436-019-00351-2
    DOI: 10.1007/s10436-019-00351-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10436-019-00351-2
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10436-019-00351-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    2. Winslow Strong & Jean-Pierre Fouque, 2011. "Diversity and arbitrage in a regulatory breakup model," Annals of Finance, Springer, vol. 7(3), pages 349-374, August.
    3. Lijun Bo & Agostino Capponi, 2014. "Bilateral credit valuation adjustment for large credit derivatives portfolios," Finance and Stochastics, Springer, vol. 18(2), pages 431-482, April.
    4. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    5. Alexander Lipton & Vadim Kaushansky & Christoph Reisinger, 2018. "Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary," Papers 1808.05311, arXiv.org, revised Aug 2018.
    6. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
    7. Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Agostino Capponi & Xu Sun & David D. Yao, 2020. "A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1127-1152, August.
    2. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    3. Justin Sirignano & Kay Giesecke, 2019. "Risk Analysis for Large Pools of Loans," Management Science, INFORMS, vol. 65(1), pages 107-121, January.
    4. Robert Elliott & Jia Shen, 2015. "Credit risk and contagion via self-exciting default intensity," Annals of Finance, Springer, vol. 11(3), pages 319-344, November.
    5. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    6. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    7. Bo, Lijun & Capponi, Agostino, 2015. "Counterparty risk for CDS: Default clustering effects," Journal of Banking & Finance, Elsevier, vol. 52(C), pages 29-42.
    8. Chen, Peimin & Wu, Chunchi, 2014. "Default prediction with dynamic sectoral and macroeconomic frailties," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 211-226.
    9. António Santos & Nuno Silva, 2019. "Sectoral concentration risk in Portuguese banks’ loan exposures to non-financial firms," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    10. John Y. Campbell & Jens Hilscher & Jan Szilagyi, 2008. "In Search of Distress Risk," Journal of Finance, American Finance Association, vol. 63(6), pages 2899-2939, December.
    11. Nicholas M. Kiefer, 2011. "Default estimation, correlated defaults, and expert information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 173-192, March.
    12. Irena Barjav{s}i'c & Stefano Battiston & Vinko Zlati'c, 2023. "Credit Valuation Adjustment in Financial Networks," Papers 2305.16434, arXiv.org.
    13. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
    14. 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.
    15. Xiao, Tim, 2018. "The Valuation of Credit Default Swap with Counterparty Risk and Collateralization," EconStor Preprints 203447, ZBW - Leibniz Information Centre for Economics.
    16. Michi Nishihara & Takashi Shibata, 2020. "Optimal capital structure and bankruptcy cascades," Discussion Papers in Economics and Business 20-10, Osaka University, Graduate School of Economics.
    17. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    18. François Gourio, 2013. "Credit Risk and Disaster Risk," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 1-34, July.
    19. Mosso-Martínez, Margarita M. & López-Herrera, Francisco, 2020. "Variables económicas y deterioro de la calidad de la cartera de hipotecas bursatilizadas en México," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 15(52), pages 47-68, Primer se.
    20. Figlewski, Stephen & Frydman, Halina & Liang, Weijian, 2012. "Modeling the effect of macroeconomic factors on corporate default and credit rating transitions," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 87-105.

    More about this item

    Keywords

    Default contagion; Mean field limit; Interacting birth-and-death process; McKean–Vlasov jump-diffusion; Propagation of chaos; Lyapunov function;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:annfin:v:15:y:2019:i:4:d:10.1007_s10436-019-00351-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.