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  • Cited by 125
  • Print publication year: 2013
  • Online publication date: June 2013

13 - Network Structure and Systemic Risk in Banking Systems



Abstract We present a quantitative methodology for analyzing the potential for contagion and systemic risk in a network of interlinked financial institutions, using a metric for the systemic importance of institutions: the Contagion Index.

We apply this methodology to a data set of mutual exposures and capital levels of financial institutions in Brazil in 2007 and 2008, and analyze the role of balance sheet size and network structure in each institution's contribution to systemic risk. Our results emphasize the contribution of heterogeneity in network structure and concentration of counterparty exposures to a given institution in explaining its systemic importance. These observations plead for capital requirements which depend on exposures, rather than aggregate balance sheet size, and which target systemically important institutions.

Keywords Default risk, domino effects, balance sheet contagion, scale-free network, default contagion, systemic risk, macro-prudential regulation, random graph.


The recent financial crisis has emphasized the importance of systemic risk, defined as macro-level risk which can impair the stability of the entire financial system. Bank failures have led in recent years to a disruption of the financial system and a significant spillover of financial distress to the larger economy (Hellwig, 2009). Regulators have had great difficulties anticipating the impact of defaults partly due to a lack of visibility on the structure of the financial system as well as a lack of a methodology for monitoring systemic risk. The complexity of the contemporary financial systems makes it a challenge to define adequate indicators of systemic risk that could help in an objective assessment of the systemic importance of financial institutions and an objective framework for assessing the efficiency of macro-prudential policies.

Acharya, V., Pedersen, L., Philippon, T., and Richardson, M. (2010). Measuring systemic risk. Working paper, New York University.
Adrian, T. and Brunnermeier, M. K. (2008). CoVaR. Staff Report 348, Federal Reserve Bank of New York.
Allen, F. and Gale, D. (2000). Financial contagion. Journal of Political Economy 108 1-33.
Amini, H., Cont, R., and Minca, A. (2010). Resilience to contagion in financial networks.
Amini, H., Cont, R., and Minca, A. (2012). Stress testing the resilience of financial networks. International Journal of Theoretical and Applied Finance, 15 (1) 1-20.
Battiston, S., Gatti, D. D., Gallegati, M., Greenwald, B. C., and Stiglitz, J. E. (2009). Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk. Working Paper 15611, National Bureau of Economic Research.
BCB (2000a). Resolution 2,723, Brazilian Central Bank, Brazil. May 31th.
BCB (2000b). Resolution 2,743, Brazilian Central Bank, Brazil. June 28th.
BCB (2007a). Resolution 3,444, Brazilian Central Bank, Brazil. February 28th.
BCB (2007b). Resolution 3,490, Brazilian Central Bank, Brazil. August 29th.
Bollobás, B., Borgs, C., Chayes, J., and Riordan, O. (2003). Directed scale-free graphs. In Symposium on Discrete Algorithms: Proceedings of the fourteenth annual ACM-SIAMsymposium on discrete algorithms, 132-139. SIAM.
Boss, M., Elsinger, H., Lehar, A., and Summer, M. (2004). The network topology of the interbank market. Quantitative Finance 4 677-684.
Clauset, A., Shalizi, C. R., and Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review 51 (4) 661–70.
Cohen, R., Havlin, S., and ben Avraham, D. (2003). Efficient immunization strategies for computer networks and populations. Phys. Rev. Lett. 91 (24) 247901.
Cont, R. (2009). Measuring systemic risk. Working paper, Columbia University.
Cont, R. and Moussa, A. (2010). Too interconnected to fail: contagion and systemic risk in financial networks. Financial Engineering Report 2010-03, Columbia University.
Cont, R. and Tanimura, E. (2008). Small world graphs: characterization and alternative constructions. Advances in Applied Probability 40 (4) 939–965.
Cont, R. and Wagalath, L. (2011). Running for the exit: Distressed selling and endogenous correlation in financial markets. Mathematical Finance, in press,
Cox, C. (2008). Letter to the Basel Committee in support of new guidance on liquidity management. Technical Report 2008-48, SEC.
De Bandt, O. and Hartmann, P. (2000). Systemic risk: A survey. Working Paper 35, European Central Bank, Frankfurt, Germany.
Degryse, H. and Nguyen, G. (2007). Interbank exposures: An empirical examination of contagion risk in the Belgian banking system. International Journal of Central Banking 3 (2) 123–171.
Eisenberg, L. and Noe, T. H. (2001). Systemic risk in financial systems. Management Science 47 (2) 236–249.
Elsinger, H., Lehar, A., and Summer, M. (2006a). Risk assessment for banking systems. Management Science 52 (9) 1301–1314.
Elsinger, H., Lehar, A., and Summer, M. (2006b). Systemically important banks: an analysis for the European banking system. International Economics and Economic Policy 3 (1) 73–89.
Freixas, X., Parigi, M., and Rochet, J. (2000). Systemic risk, interbank relations and liquidity provision by the central bank. Journal of Money Credit and Banking 32 (3) 611–638.
Furfine, C. H. (2003). Interbank exposures: Quantifying the risk of contagion. Journal of Money, Credit and Banking 35 (1) 111–128.
Gai, P. and Kapadia, S. (2010). Contagion in financial networks. Proceedings of the Royal Society A 466 (2120) 2401–2423.
Haldane, A. (2009). Rethinking the financial network. Speech, Bank of England.
Hellwig, M. (1995). Systemic aspects of risk management in banking and finance. Swiss Journal of Economics and Statistics 131 (IV) 723-737.
Hellwig, M. (2009). Systemic risk in the financial sector: An analysis of the subprime- mortgage financial crisis. De Economist 157 (2) 129–207.
Huang, X.-L., Zou, F.-T., and Ma, F.-Y. (2007). Targeted local immunization in scale-free peer-to-peer networks. J. Comput. Sci. Technol. 22 (3) 457–468.
Lehar, A. (2005). Measuring systemic risk: A risk management approach, Journal of Banking & Finance 29 (10) 2577–2603.
Liu, M. and Staum, J. (2011). Systemic risk components in a network model of contagion. Working paper, Northwestern University.
Lo, A. (2011). Complexity, concentration and contagion: A comment. Journal of Monetary Economics 58 (5) 471–479.
Madar, N., Kalisky, T., Cohen, R., Ben-avraham, D., and Havlin, S. (2004). Immunization and epidemic dynamics in complex networks. The European Physical Journal B 38 4269-276.
Mistrulli, P. E. (2007). Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns. Bank of Italy Research Paper Series – Temi di Discussione 641, Bank of Italy, Economic Research Department, Rome, Italy.
Müller, J. (2006). Interbank credit lines as a channel of contagion. Journal of Financial Services Research 29 (1) 37–60.
Nier, E., Yang, J., Yorulmazer, T., and Alentorn, A. (2007). Network models and financial stability. Journal ofEconomic Dynamics and Control 31 2033-2060.
Sheldon, G. and Maurer, M. (1998). Interbank lending and systemic risk: An empirical analysis for switzerland. Swiss Journal ofEconomics and Statistics 134 (IV) 685704.
Tarashev, N., Borio, C. E., and Tsatsaronis, K. (2010). Attributing systemic risk to individual institutions. Working Paper 308, BIS.
Upper, C. (2011). Simulation methods to assess the danger of contagion in interbank markets. Journal of Financial Stability 7 (3) 111–125.
Upper, C. and Worms, A. (2004). Estimating bilateral exposures in the German interbank market: Is there a danger of contagion?European Economic Review 48 (4) 827–849.
van Lelyveld, I. and Liedorp, F. (2006). Interbank contagion in the dutch banking sector: A sensitivity analysis. International Journal of Central Banking 2 (2) 99–133.
Watts, D. J. and Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature 393 (4) 440–442.
Wells, S. (2004). Financial interlinkages in the United Kingdom's interbank market and the risk of contagion. Working Paper 230, Bank of England, London.
Zhou, H., Huang, X., and Zhu, H. (2009). A framework for assessing the systemic risk of major financial institutions. Journal of Banking and Finance 33 2036-2049.