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

Gerald SilverbergUNU-MERIT and IIASA

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), arXiv:cond-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: 259–278.

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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

Multitiered Italian interbank network

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• Agata Aleksiejuk, Janusz A. Holyst and Gueorgi Kossinets, 2001, Self-organized criticality in a model of collective bank bankruptcies, arXiv:cond-mat/0111586v2

• Michael Boss, Martin Summer, Stefan Thurner, 2004, Contagion Flow Through Banking Networks, arXiv:cond-mat/0403167v1

• Giulia Iori, Saqib Jafarey, Francisco G. Padilla, 2006, Systemic risk on the interbank market, JEBO, 61: 525–542

• Erlend Niera,, Jing Yanga, Tanju Yorulmazera,• Amadeo Alentorn, 2007, Network models and financial

stability, Journal of Economic Dynamics & Control 31: 2033–2060

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Network Models of Financial Contagion: Literature

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)

15Exponential failure avalanche distribution in two-dimensional lattices

Power-Law Distribution for Dimension 3

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Power-Law Distribution for Dimension 4

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