Mapping systemic risk: critical degree and failures distribution in financial networks
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. Using a mean-field approach, we obtain a closed-form formula for the "critical degree", viz. the number of creditors per bank below which an individual shock can propagate throughout the network. We relate the failures distribution (probability that a single shock induces $F$ failures) to the degree distribution (probability that a bank has $k$ creditors), showing in particular that the former is fat-tailed whenever the latter is. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hans Degryse & Grégory Nguyen, 2007. "Interbank Exposures: An Empirical Examination of Contagion Risk in the Belgian Banking System," International Journal of Central Banking, International Journal of Central Banking, vol. 3(2), pages 123-171, June.
- Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015.
"Systemic Risk and Stability in Financial Networks,"
American Economic Review,
American Economic Association, vol. 105(2), pages 564-608, February.
- Xavier Freixas & Antoine Martin & David Skeie, 2010.
"Bank liquidity, interbank markets and monetary policy,"
Economics Working Papers
1202, Department of Economics and Business, Universitat Pompeu Fabra.
- Xavier Freixas & Antoine Martin & David Skeie, 2011. "Bank Liquidity, Interbank Markets, and Monetary Policy," Review of Financial Studies, Society for Financial Studies, vol. 24(8), pages 2656-2692.
- Xavier Freixas & Antoine Martin & David Skeie, 2010. "Bank Liquidity, Interbank Markets and Monetary Policy," Working Papers 429, Barcelona Graduate School of Economics.
- Xavier Freixas & Antoine Martin & David R. Skeie, 2009. "Bank liquidity, interbank markets, and monetary policy," Staff Reports 371, Federal Reserve Bank of New York.
- Freixas, X. & Martin, A. & Skeie, D., 2010. "Bank Liquidity, Interbank Markets, and Monetary Policy," Discussion Paper 2010-35S, Tilburg University, Center for Economic Research.
- Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
- John B. Taylor & John C. Williams, 2009.
"A black swan in the money market,"
Federal Reserve Bank of San Francisco, issue Jan.
- Furfine, Craig H, 2003. " Interbank Exposures: Quantifying the Risk of Contagion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(1), pages 111-28, February.
- John Taylor & John Williams, 2008. "Further Results on a Black Swan in the Money Market," Discussion Papers 07-046, Stanford Institute for Economic Policy Research.
- N. Lesca, 2010. "Introduction," Post-Print halshs-00640602, HAL.
- Soramäki, Kimmo & Bech, Morten L. & Arnold, Jeffrey & Glass, Robert J. & Beyeler, Walter E., 2007.
"The topology of interbank payment flows,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 379(1), pages 317-333.
- Billio, Monica & Getmansky, Mila & Lo, Andrew W. & Pelizzon, Loriana, 2012.
"Econometric measures of connectedness and systemic risk in the finance and insurance sectors,"
Journal of Financial Economics,
Elsevier, vol. 104(3), pages 535-559.
- Monica Billio & Mila Getmansky & Andrew W. Lo & Loriana Pelizzon, 2011. "Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors," Working Papers 2011_21, Department of Economics, University of Venice "Ca' Foscari".
- Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012.
"Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 36(8), pages 1121-1141.
- Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce C. Greenwald & Joseph E. Stiglitz, 2009. "Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk," NBER Working Papers 15611, National Bureau of Economic Research, Inc.
- Bech, Morten L. & Atalay, Enghin, 2008.
"The topology of the federal funds market,"
Working Paper Series
0986, European Central Bank.
- Bech, Morten L. & Atalay, Enghin, 2010. "The topology of the federal funds market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5223-5246.
- Nier, Erlend & Yang, Jing & Yorulmazer, Tanju & Alentorn, Amadeo, 2008.
"Network models and financial stability,"
Bank of England working papers
346, Bank of England.
- Minoiu, Camelia & Reyes, Javier A., 2013. "A network analysis of global banking: 1978–2010," Journal of Financial Stability, Elsevier, vol. 9(2), pages 168-184.
- Dimitrios Bisias & Mark Flood & Andrew W. Lo & Stavros Valavanis, 2012.
"A Survey of Systemic Risk Analytics,"
12-01, Office of Financial Research, US Department of the Treasury.
- Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
- De Bandt, Olivier & Hartmann, Philipp, 2000.
"Systemic risk: A survey,"
Working Paper Series
0035, European Central Bank.
- Michael Boss & Helmut Elsinger & Martin Summer & Stefan Thurner, 2004. "Network topology of the interbank market," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 677-684.
- John Kambhu & Scott Weidman & Neel Krishnan, 2007. "New directions for understanding systemic risk: a report on a conference cosponsored by the Federal Reserve Bank of New York and the National Academy of Sciences," Economic Policy Review, Federal Reserve Bank of New York, issue Nov, pages i-83.
- Mistrulli, Paolo Emilio, 2011.
"Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns,"
Journal of Banking & Finance,
Elsevier, vol. 35(5), pages 1114-1127, May.
- Paolo Emilio Mistrulli, 2007. "Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns," Temi di discussione (Economic working papers) 641, Bank of Italy, Economic Research and International Relations Area.
- Adam B. Ashcraft & Darrell Duffie, 2007. "Systemic Illiquidity in the Federal Funds Market," American Economic Review, American Economic Association, vol. 97(2), pages 221-225, May.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1402.4783. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.