##
**Network models and financial stability.**
*(English)*
Zbl 1201.91245

Summary: Systemic risk is a key concern for central banks charged with safeguarding overall financial stability. In this paper we investigate how systemic risk is affected by the structure of the financial system. We construct banking systems that are composed of a number of banks that are connected by interbank linkages. We then vary the key parameters that define the structure of the financial system – including its level of capitalisation, the degree to which banks are connected, the size of interbank exposures and the degree of concentration of the system – and analyse the influence of these parameters on the likelihood of knock-on defaults. First, we find that the better capitalised banks are, the more resilient is the banking system against contagious defaults and this effect is non-linear. Second, the effect of the degree of connectivity is non-monotonic, i.e. initially a small increase in connectivity increases the contagion effect; but after a certain threshold value, connectivity improves the ability of a banking system to absorb shocks. Third, the size of interbank liabilities tends to increase the risk of knock-on default, even if banks hold capital against such exposures. Fourth, more concentrated banking systems are shown to be prone to larger systemic risk, all else equal. In an extension to the main analysis we study how liquidity effects interact with banking structure to produce a greater chance of systemic breakdown. We finally consider how the risk of contagion might depend on the degree of asymmetry (tiering) inherent in the structure of the banking system. A number of our results have important implications for public policy, which this paper also draws out.

### MSC:

91G99 | Actuarial science and mathematical finance |

91B64 | Macroeconomic theory (monetary models, models of taxation) |

PDFBibTeX
XMLCite

\textit{E. Nier} et al., J. Econ. Dyn. Control 31, No. 6, 2033--2060 (2007; Zbl 1201.91245)

Full Text:
DOI

### References:

[1] | Acharya, V., Yorulmazer, T., 2007. Cash-in-the-market pricing and optimal bank bailout policy. Review of Financial Studies, forthcoming.; Acharya, V., Yorulmazer, T., 2007. Cash-in-the-market pricing and optimal bank bailout policy. Review of Financial Studies, forthcoming. |

[2] | Allen, F., Gale, D., 1994. Limited market participation and volatility of asset prices. American Economic Review 84 (4), 933-955.; Allen, F., Gale, D., 1994. Limited market participation and volatility of asset prices. American Economic Review 84 (4), 933-955. |

[3] | Allen, F., Gale, D., 1998. Optimal financial crises. Journal of Finance 53 (4), 1245-1284.; Allen, F., Gale, D., 1998. Optimal financial crises. Journal of Finance 53 (4), 1245-1284. |

[4] | Allen, F.; Gale, D., Financial contagion, Journal of Political Economy, 108, 1-33 (2000) |

[5] | Barabasi, A.-L.; Albert, R., Emergence of scaling in random networks, Science, 286, 508-512 (1999) · Zbl 1226.05223 |

[6] | Barth, J. R.; Caprio, G.; Levine, R., Rethinking Bank Regulation—Till Angels Govern (2006), Cambridge University Press: Cambridge University Press Cambridge |

[7] | Bhattacharya, S., Gale, D., 1987. Preference shocks, liquidity, and central bank policy. New Approaches to Monetary Economics: Proceedings of the Second International Symposium in Economic Theory and Econometrics. Cambridge University Press, Cambridge, New York, and Melbourne. pp. 69-88.; Bhattacharya, S., Gale, D., 1987. Preference shocks, liquidity, and central bank policy. New Approaches to Monetary Economics: Proceedings of the Second International Symposium in Economic Theory and Econometrics. Cambridge University Press, Cambridge, New York, and Melbourne. pp. 69-88. |

[8] | Boss, M., Elsinger, H., Summer, M., Thurner, S., 2003. The network topology of the interbank market. arXiv:cond-mat/0309582v1, 25 September 2003.; Boss, M., Elsinger, H., Summer, M., Thurner, S., 2003. The network topology of the interbank market. arXiv:cond-mat/0309582v1, 25 September 2003. |

[9] | Boss, M., Elsinger, H., Summer, M., Thurner, S., 2004. An empirical analysis of the network structure of the Austrian interbank market. Oesterreichische Nationalbank Financial Stability Report, June, 77-87.; Boss, M., Elsinger, H., Summer, M., Thurner, S., 2004. An empirical analysis of the network structure of the Austrian interbank market. Oesterreichische Nationalbank Financial Stability Report, June, 77-87. |

[10] | Calomiris, C.W., Gorton, G., 1991. The origins of banking panics: models, facts, and bank regulation. Financial Markets and Financial Crises, A National Bureau of Economic Research Project Report. University of Chicago University Press, Chicago and London.; Calomiris, C.W., Gorton, G., 1991. The origins of banking panics: models, facts, and bank regulation. Financial Markets and Financial Crises, A National Bureau of Economic Research Project Report. University of Chicago University Press, Chicago and London. |

[11] | Chen, Y., Banking panics: the role of the first-come, first-served rule and information externalities, Journal of Political Economy, 107, 5, 946-968 (1999) |

[12] | Cifuentes, R.; Ferrucci, G.; Shin, H., Liquidity risk and contagion, Journal of the European Economic Association, 3, 556-566 (2005) |

[13] | De Bandt, O., Hartmann, P., 2000. Systemic risk: a survey. ECB Working Paper No. 35, November 2000.; De Bandt, O., Hartmann, P., 2000. Systemic risk: a survey. ECB Working Paper No. 35, November 2000. |

[14] | Demirgue-Kunt, A.; Detragiache, E., Does deposit insurance increase banking system stability? An empirical investigation, Journal of Monetary Economics, 49, 1373-1406 (2002) |

[15] | Diamond, D.; Dybvig, P., Bank runs, deposit insurance and liquidity, Journal of Political Economy, 91, 401-419 (1983) · Zbl 1341.91135 |

[16] | Eboli, M., 2004. Systemic risk in financial networks: a graph theoretic approach. Mimeo Universita di Chieti Pescara.; Eboli, M., 2004. Systemic risk in financial networks: a graph theoretic approach. Mimeo Universita di Chieti Pescara. |

[17] | Eisenberg, L.; Noe, T., Systemic risk in financial systems, Management Science, 47, 236-249 (2001) · Zbl 1232.91688 |

[18] | Elsinger, H.; Lehar, A.; Summer, M., Risk assessment for banking systems, Management Science, 52, 9, 1301-1314 (2006) · Zbl 1232.91689 |

[19] | Erdös, P.; Rényi, A., On random graphs, Publicationes Mathematicae, 6, 290-297 (1959) · Zbl 0092.15705 |

[20] | Flannery, M., Financial crises, payments system problems and discount window lending, Journal of Money, Credit and Banking, 28, 804-824 (1996) |

[21] | Furfine, C.H., 1999. Interbank exposures: quantifying the risk of contagion. BIS Working Paper No. 70, Basel.; Furfine, C.H., 1999. Interbank exposures: quantifying the risk of contagion. BIS Working Paper No. 70, Basel. |

[22] | Grassberger, P., On the critical behaviour of the general epidemic process and dynamical percolation, Mathematical Biosciences, 63, 157-172 (1983) · Zbl 0531.92027 |

[23] | Harrison, S., Lasaosa, A., Tudela, M., 2005. Tiering in UK payment systems—credit risk implications. Bank of England Financial Stability Review, December 63-72.; Harrison, S., Lasaosa, A., Tudela, M., 2005. Tiering in UK payment systems—credit risk implications. Bank of England Financial Stability Review, December 63-72. |

[24] | Hoggarth, G.; Reis, R.; Saporta, V., Costs of banking system instability: some empirical evidence, Journal of Banking and Finance, 26, 5, 825-855 (2002) |

[25] | Iyer, R., Peydro-Alcalde, J.L., 2006. Interbank contagion: evidence from real transactions. Mimeo, University of Amsterdam.; Iyer, R., Peydro-Alcalde, J.L., 2006. Interbank contagion: evidence from real transactions. Mimeo, University of Amsterdam. |

[26] | Lelyveld, I.; Liedorp, F., Interbank contagion in the Dutch banking sector: a sensitivity analysis, International Journal of Central Banking, 2, 2, 99-133 (2006) |

[27] | Mistrulli, P., Interbank lending patterns and financial contagion (2005), Mimeo: Mimeo Banca d’Italia |

[28] | Newman, M.E.J., 2003. Random graphs as models of networks. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA.; Newman, M.E.J., 2003. Random graphs as models of networks. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA. |

[29] | Nier, E., Baumann, U., 2006. Market discipline, disclosure and moral hazard in banking. Journal of Financial Intermediation 15, 332-361.; Nier, E., Baumann, U., 2006. Market discipline, disclosure and moral hazard in banking. Journal of Financial Intermediation 15, 332-361. |

[30] | Rochet, J.-C.; Tirole, J., Interbank lending and systemic risk, Journal of Money, Credit and Banking, 28, 4, 733-762 (1996) |

[31] | Sheldon, G.; Maurer, M., Interbank lending and systemic risk: an empirical analysis of Switzerland, Swiss Journal of Economics and Statistics, 134, 4.2, 685-704 (1998) |

[32] | Upper, C.; Worms, A., Estimating bilateral exposures in the German interbank market: is there a danger of contagion? European Economic Review, 48, 827-849 (2004) |

[33] | Watts, D.J., 2002. A simple model of global cascades on random networks. Santa Fe Institute, Santa Fe, NM, February 14, 2002.; Watts, D.J., 2002. A simple model of global cascades on random networks. Santa Fe Institute, Santa Fe, NM, February 14, 2002. · Zbl 1022.90001 |

[34] | Watts, D. J.; Strogatz, S. H., Collective dynamics of ‘small-world’ networks, Nature, 393, 440-442 (1998) · Zbl 1368.05139 |

[35] | Wells, S., 2002. UK interbank exposures: systemic risk implications. Bank of England Financial Stability Review, December, 175-182.; Wells, S., 2002. UK interbank exposures: systemic risk implications. Bank of England Financial Stability Review, December, 175-182. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.