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A framework for analyzing contagion in banking networks

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  • Thomas R. Hurd
  • James P. Gleeson
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    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.

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    File URL: http://arxiv.org/pdf/1110.4312
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.4312.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.4312

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    Web page: http://arxiv.org/

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    1. 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.
    2. Nier, Erlend & Yang, Jing & Yorulmazer, Tanju & Alentorn, Amadeo, 2008. "Network models and financial stability," Bank of England working papers 346, Bank of England.
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    Cited by:
    1. Thomas R. Hurd & Davide Cellai & Huibin Cheng & Sergey Melnik & Quentin Shao, 2013. "Illiquidity and Insolvency: a Double Cascade Model of Financial Crises," Papers 1310.6873, arXiv.org, revised Apr 2014.
    2. 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.

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