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A framework for analyzing contagion in banking networks

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  • Thomas R. Hurd
  • James P. Gleeson

Abstract

A probabilistic framework is introduced that represents stylized banking networks and aims to predict the size of contagion events. In contrast to previous work on random financial networks, which assumes independent connections between banks, the possibility of disassortative edge probabilities (an above average tendency for small banks to link to large banks) is explicitly incorporated. We give a probabilistic analysis of the default cascade triggered by shocking the network. We find that the cascade can be understood as an explicit iterated mapping on a set of edge probabilities that converges to a fixed point. A cascade condition is derived that characterizes whether or not an infinitesimal shock to the network can grow to a finite size cascade, in analogy to the basic reproduction number $R_0$ in epidemic modeling. It provides an easily computed measure of the systemic risk inherent in a given banking network topology. An analytic formula is given for the frequency of global cascades, derived from percolation theory on the random network. Two simple examples are used to demonstrate that edge-assortativity can have a strong effect on the level of systemic risk as measured by the cascade condition. Although the analytical methods are derived for infinite networks, large-scale Monte Carlo simulations are presented that demonstrate the applicability of the results to finite-sized networks. Finally, we propose a simple graph theoretic quantity, which we call "graph-assortativity", that seems to best capture systemic risk.

Suggested Citation

  • Thomas R. Hurd & James P. Gleeson, 2011. "A framework for analyzing contagion in banking networks," Papers 1110.4312, arXiv.org.
  • Handle: RePEc:arx:papers:1110.4312
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    References listed on IDEAS

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    1. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
    2. Upper, Christian, 2011. "Simulation methods to assess the danger of contagion in interbank markets," Journal of Financial Stability, Elsevier, vol. 7(3), pages 111-125, August.
    3. Nier, Erlend & Yang, Jing & Yorulmazer, Tanju & Alentorn, Amadeo, 2007. "Network models and financial stability," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2033-2060, June.
    4. N. Lesca, 2010. "Introduction," Post-Print halshs-00640602, HAL.
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    Citations

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    Cited by:

    1. Caccioli, Fabio & Shrestha, Munik & Moore, Cristopher & Farmer, J. Doyne, 2014. "Stability analysis of financial contagion due to overlapping portfolios," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 233-245.
    2. 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.
    3. T. R. Hurd & Davide Cellai & Sergey Melnik & Quentin H. Shao, 2016. "Double Cascade Model Of Financial Crises," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-27, August.
    4. Thomas R. Hurd & Davide Cellai & Sergey Melnik & Quentin Shao, 2013. "Double Cascade Model of Financial Crises," Papers 1310.6873, arXiv.org, revised Sep 2016.
    5. Stefano Battiston & Marco D'Errico & Stefano Gurciullo & Guido Caldarelli, 2015. "Leveraging the network: a stress-test framework based on DebtRank," Papers 1503.00621, arXiv.org, revised Feb 2016.
    6. Oliver Kley & Claudia Kluppelberg & Lukas Reichel, 2014. "Systemic risk through contagion in a core-periphery structured banking network," Papers 1406.6575, arXiv.org.
    7. Leonidov, A. & Rumyantsev, E., 2013. "Russian Interbank Systemic Risks Assessment from the Network Topology Point of View," Journal of the New Economic Association, New Economic Association, vol. 19(3), pages 65-80.
    8. Marco Bardoscia & Stefano Battiston & Fabio Caccioli & Guido Caldarelli, 2015. "DebtRank: A microscopic foundation for shock propagation," Papers 1504.01857, arXiv.org, revised Jun 2015.

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