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Mapping systemic risk: critical degree and failures distribution in financial networks

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  • Matteo Smerlak
  • Brady Stoll
  • Agam Gupta
  • James S. Magdanz
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    Abstract

    The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. Using a mean-field approach, we obtain a closed-form formula for the "critical degree", viz. the number of creditors per bank below which an individual shock can propagate throughout the network. We relate the failures distribution (probability that a single shock induces $F$ failures) to the degree distribution (probability that a bank has $k$ creditors), showing in particular that the former is fat-tailed whenever the latter is. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.

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    File URL: http://arxiv.org/pdf/1402.4783
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1402.4783.

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    Date of creation: Feb 2014
    Date of revision: Mar 2014
    Handle: RePEc:arx:papers:1402.4783

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    Web page: http://arxiv.org/

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    5. Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce C. Greenwald & Joseph E. Stiglitz, 2009. "Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk," NBER Working Papers 15611, National Bureau of Economic Research, Inc.
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    16. John Taylor & John Williams, 2008. "Further Results on a Black Swan in the Money Market," Discussion Papers 07-046, Stanford Institute for Economic Policy Research.
    17. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
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