Phase Transitions in Networked Financial Systems: An Explanation of Financial Meltdown? Gerald Silverberg UNU-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/ v1. – 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. 2

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 3

Multiscaling of degree distributions: results for Austria 4

5 Scaling in the Italian interbank network

Multitiered Italian interbank network 6

Agata Aleksiejuk, Janusz A. Holyst and Gueorgi Kossinets, 2001, Self-organized criticality in a model of collective bank bankruptcies, arXiv:cond-mat/ v2 Michael Boss, Martin Summer, Stefan Thurner, 2004, Contagion Flow Through Banking Networks, arXiv:cond- mat/ v1 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– 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 8

Dynamics of Bankruptcy Contagion 9

Effects of Net Worth (Equity) on Contagion Mortality (Nier et al. 2007) 10

Effects of Intermediation on Bank Failures (Nier et al. 2007) 11

Effects of Connectivity (Nier et al. 2007) 12

Contervailing Effects of Risk-Sharing and Contagion with Connectivity (Iori et al. 2006) 13

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. 14

Self-Organized Criticality in Lattice-Networked Interbank Lending in Dimensions 2,3, and 4 (Aleksiejuk et al. 2001, Failure with replacement) 15 Exponential failure avalanche distribution in two-dimensional lattices

Power-Law Distribution for Dimension 3 16

Power-Law Distribution for Dimension 4 17