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A framework for analyzing contagion in assortative banking networks

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  • Thomas R Hurd
  • James P Gleeson
  • Sergey Melnik

Abstract

We introduce a probabilistic framework that represents stylized banking networks with the aim of predicting the size of contagion events. Most previous work on random financial networks assumes independent connections between banks, whereas our framework explicitly allows for (dis)assortative edge probabilities (i.e., a tendency for small banks to link to large banks). We analyze default cascades triggered by shocking the network and find that the cascade can be understood as an explicit iterated mapping on a set of edge probabilities that converges to a fixed point. We derive a cascade condition, analogous to the basic reproduction number R0 in epidemic modelling, that characterizes whether or not a single initially defaulted bank can trigger a cascade that extends to a finite fraction of the infinite network. This cascade condition is an easily computed measure of the systemic risk inherent in a given banking network topology. We use percolation theory for random networks to derive a formula for the frequency of global cascades. These analytical results are shown to provide limited quantitative agreement with Monte Carlo simulation studies of finite-sized networks. We show that edge-assortativity, the propensity of nodes to connect to similar nodes, can have a strong effect on the level of systemic risk as measured by the cascade condition. However, the effect of assortativity on systemic risk is subtle, and we propose a simple graph theoretic quantity, which we call the graph-assortativity coefficient, that can be used to assess systemic risk.

Suggested Citation

  • Thomas R Hurd & James P Gleeson & Sergey Melnik, 2017. "A framework for analyzing contagion in assortative banking networks," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-20, February.
  • Handle: RePEc:plo:pone00:0170579
    DOI: 10.1371/journal.pone.0170579
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    Citations

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    Cited by:

    1. Nils Detering & Thilo Meyer-Brandis & Konstantinos Panagiotou & Daniel Ritter, 2018. "Financial Contagion in a Generalized Stochastic Block Model," Papers 1803.08169, arXiv.org, revised Dec 2019.
    2. Fabio Caccioli & Paolo Barucca & Teruyoshi Kobayashi, 2018. "Network models of financial systemic risk: a review," Journal of Computational Social Science, Springer, vol. 1(1), pages 81-114, January.
    3. Michel Alexandre & Gilberto Tadeu Lima & Luca Riccetti & Alberto Russo, 2023. "The financial network channel of monetary policy transmission: an agent-based model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 533-571, July.
    4. Daniel Ritter, 2019. "Mathematical Modeling of Systemic Risk in Financial Networks: Managing Default Contagion and Fire Sales," Papers 1911.07313, arXiv.org.
    5. T. R. Hurd, 2019. "Systemic Cascades On Inhomogeneous Random Financial Networks," Papers 1909.09239, arXiv.org.
    6. Mikhail Stolbov & Daniil Parfenov, 2023. "Credit risk linkages in the international banking network, 2000–2019," Risk Management, Palgrave Macmillan, vol. 25(3), pages 1-38, September.
    7. Abduraimova, Kumushoy & Nahai-Williamson, Paul, 2021. "Solvency distress contagion risk: network structure, bank heterogeneity and systemic resilience," Bank of England working papers 909, Bank of England.

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