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On the Computational Complexity of Measuring Global Stability of Banking Networks

  • Piotr Berman
  • Bhaskar DasGupta
  • Lakshmi Kaligounder
  • Marek Karpinski
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    Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreading of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures, define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.

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    Paper provided by in its series Papers with number 1110.3546.

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    Date of creation: Oct 2011
    Date of revision: Mar 2013
    Publication status: Published in Algorithmica, 70(4), 595-647, 2014
    Handle: RePEc:arx:papers:1110.3546
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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. Douglas M. Gale & Shachar Kariv, 2007. "Financial Networks," American Economic Review, American Economic Association, vol. 97(2), pages 99-103, May.
    3. Roger Lagunoff & Stacey L. Schreft, 1998. "A model of financial fragility," Research Working Paper 98-01, Federal Reserve Bank of Kansas City.
    4. Krishnamurthy, Arvind, 2000. "Comment on Systemic Risk, Interbank Relations, and Liquidity Provision by the Central Bank," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(3), pages 639-40, August.
    5. Michele Manna & Carmela Iazzetta, 2009. "The topology of the interbank market: developments in Italy since 1990," Temi di discussione (Economic working papers) 711, Bank of Italy, Economic Research and International Relations Area.
    6. F.R. Liedorp & L. Medema & M. Koetter & R.H. Koning & I. van Lelyveld, 2010. "Peer monitoring or contagion? Interbank market exposure and bank risk," DNB Working Papers 248, Netherlands Central Bank, Research Department.
    7. Xavier Freixas & Bruno Parigi & Jean Charles Rochet, 1998. "Systemic risk, interbank relations and liquidity provision by the Central Bank," Economics Working Papers 440, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 1999.
    8. basab dasgupta, 2005. "Capital Accumulation in the Presence of Informal Credit Contract: Does Incentive Mechanism Work Better than Credit Rationing Under Asymmetric Information?," Computing in Economics and Finance 2005 366, Society for Computational Economics.
    9. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-23.
    10. Franklin Allen & Douglas Gale, 1999. "Financial Contagion," Levine's Working Paper Archive 2092, David K. Levine.
    11. Castiglionesi, F. & Navarro, N., 2007. "Optimal Fragile Financial Networks," Discussion Paper 2007-100, Tilburg University, Center for Economic Research.
    12. Yaron Leitner, 2005. "Financial Networks: Contagion, Commitment, and Private Sector Bailouts," Journal of Finance, American Finance Association, vol. 60(6), pages 2925-2953, December.
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