Phase Transitions in Networked Financial Systems: An Explanation of Financial Meltdown

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Phase Transitions in Networked Financial Systems
An Explanation of Financial Meltdown?

• Gerald Silverberg
• UNU-MERIT and IIASA

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What is known about financial networks?

• The interbank lending market has been studied
  most closely, e.g.
• M. Boss, H. Elsinger, M. Summer, S. Thurner,
  2003, The Network Topology of the Interbank
  Market (Austria), arXivcond-mat/0309582v1.
• G. Iori,, G. De Masi, O. V. Precup, G. Gabbi, G.
  Caldarelli, 2008, A network analysis of the
  Italian overnight money market, JEBO 32 259278.

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• Interbank networks are roughly scale-free but
  have low clustering, thus they are hierarchical,
  multitiered networks, with large banks located
  centrally and small banks in the periphery
  results for Austria

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• Multiscaling of degree distributions results for
  Austria

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• Scaling in the Italian interbank network

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Multitiered Italian interbank network
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Network Models of Financial Contagion Literature

• Agata Aleksiejuk, Janusz A. Holyst and Gueorgi
  Kossinets, 2001, Self-organized criticality in a
  model of collective bank bankruptcies,
  arXivcond-mat/0111586v2
• Michael Boss, Martin Summer, Stefan Thurner,
  2004, Contagion Flow Through Banking Networks,
  arXivcond-mat/0403167v1
• Giulia Iori, Saqib Jafarey, Francisco G. Padilla,
  2006, Systemic risk on the interbank market,
  JEBO, 61 525542
• Erlend Niera,, Jing Yanga, Tanju Yorulmazera,
• Amadeo Alentorn, 2007, Network models and
  financial stability, Journal of Economic Dynamics
  Control 31 20332060

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Network Models of Financial Contagion
Restrictions

• Interbank (overnight) lending markets only
  reflect a small and short-term component of
  financial institutions balance sheets
• In particular, they leave out securitized debt
  and the dynamics of collatarized leverage which
  have been at the center of both the 1929 and the
  present financial crises
• Contagion models have mostly been studied on
  lattices or Erdos-Renyi random graphs, while we
  know from the previous results that real
  financial networks are much more complex
• There are different elements of systemic risk
  incorporated in the models, e.g., whether
  firesales of assets depresses values as a
  function of volume

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Dynamics of Bankruptcy Contagion
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Effects of Net Worth (Equity) on Contagion
Mortality (Nier et al. 2007)
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Effects of Intermediation on Bank Failures (Nier
et al. 2007)
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Effects of Connectivity (Nier et al. 2007)
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Contervailing Effects of Risk-Sharing and
Contagion with Connectivity (Iori et al. 2006)
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Effects of Topology on Contagion (Boss et al.
2004) Contagion impact as a function of relative
node betweenness for the L matrix. Below a value
of B(i) of 0.6 no contagion impact is found.
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Self-Organized Criticality in Lattice-Networked
Interbank Lending in Dimensions 2,3, and 4
(Aleksiejuk et al. 2001, Failure with replacement)
Exponential failure avalanche distribution in
two-dimensional lattices
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Power-Law Distribution for Dimension 3
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Power-Law Distribution for Dimension 4