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Illiquidity and Insolvency: a Double Cascade Model of Financial Crises

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  • Thomas R. Hurd
  • Davide Cellai
  • Huibin Cheng
  • Sergey Melnik
  • Quentin Shao
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    Abstract

    In the aftermath of the interbank market collapse of 2007-08, the scope of systemic risk research has broadened to encompass a wide range of channels, notably asset correlations, default contagion, illiquidity contagion, and asset firesales. In current models of systemic risk, two facets of contagion, namely funding illiquidity and insolvency, are treated as two distinct and separate phenomena. The main goal of the double cascade model we introduce is to integrate these two facets. In a default cascade, insolvency of a given bank will create a shock to the asset side of the balance sheet of each of its creditor banks. Under some circumstances, such "downstream" shocks can cause further insolvencies that may build up to create a global insolvency cascade. On the other hand, in a stress cascade, illiquidity that hits a given bank will create a shock to the liability side of the balance sheet of each of its debtor banks. Such "upstream" shocks can cause further illiquidity stresses that may build up to create a global illiquidity cascade. Our paper introduces a deliberately simplified network model of insolvency and illiquidity that can quantify how illiquidity or default of one bank influences the overall level of liquidity stress and default in the network. Under an assumption we call "locally tree-like independence", we derive large-network asymptotic cascade formulas. Results of numerical experiments then demonstrate that these asymptotic formulas agree qualitatively with Monte Carlo results for large finite networks, and quantitatively except when the system is placed in an exceptional "knife-edge" configuration. These experiments illustrate clearly our main conclusion that in financial networks, the average default probability is inversely related to strength of banks' stress response and therefore to the overall level of stress in the network.

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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1310.6873.

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    Date of creation: Oct 2013
    Date of revision: Apr 2014
    Handle: RePEc:arx:papers:1310.6873

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    Web page: http://arxiv.org/

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    1. Nier, Erlend & Yang, Jing & Yorulmazer, Tanju & Alentorn, Amadeo, 2008. "Network models and financial stability," Bank of England working papers 346, Bank of England.
    2. Gai, Prasanna & Haldane, Andrew & Kapadia, Sujit, 2011. "Complexity, concentration and contagion," Journal of Monetary Economics, Elsevier, vol. 58(5), pages 453-470.
    3. Thomas R. Hurd & James P. Gleeson, 2011. "A framework for analyzing contagion in banking networks," Papers 1110.4312, arXiv.org.
    4. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    5. Rodrigo Cifuentes & Hyun Song Shin & Gianluigi Ferrucci, 2005. "Liquidity Risk and Contagion," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 556-566, 04/05.
    6. Adrian, Tobias & Shin, Hyun Song, 2010. "Liquidity and leverage," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 418-437, July.
    7. Rodrigo Cifuentes & Gianluigi Ferrucci & Hyun Song Shin, 2005. "Liquidity risk and contagion," Bank of England working papers 264, Bank of England.
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