Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year

Cite Score 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.455
Source Normalized Impact per Paper (SNIP) 2017: 0.853

Mathematical Citation Quotient (MCQ) 2017: 0.32

See all formats and pricing
More options …
Volume 33, Issue 3-4


Leveraging the network: A stress-test framework based on DebtRank

Stefano Battiston
  • Corresponding author
  • Department of Banking and Finance, University of Zurich, Plattenstrasse 14,8032 Zürich, Switzerland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Guido Caldarelli
  • IMT Alti Studi Lucca, ISC-CNR, Rome, Italy; and LIMS London, United Kingdom of Great Britain and Northern Ireland
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Marco D’Errico / Stefano Gurciullo
Published Online: 2016-08-19 | DOI: https://doi.org/10.1515/strm-2015-0005


We develop a novel stress-test framework to monitor systemic risk in financial systems. The modular structure of the framework allows to accommodate for a variety of shock scenarios, methods to estimate interbank exposures and mechanisms of distress propagation. The main features are as follows. First, the framework allows to estimate and disentangle not only first-round effects (i.e. shock on external assets) and second-round effects (i.e. distress induced in the interbank network), but also third-round effects induced by possible fire sales. Second, it allows to monitor at the same time the impact of shocks on individual or groups of financial institutions as well as their vulnerability to shocks on counterparties or certain asset classes. Third, it includes estimates for loss distributions, thus combining network effects with familiar risk measures such as VaR and CVaR. Fourth, in order to perform robustness analyses and cope with incomplete data, the framework features a module for the generation of sets of networks of interbank exposures that are coherent with the total lending and borrowing of each bank. As an illustration, we carry out a stress-test exercise on a dataset of listed European banks over the years 2008–2013. We find that second-round and third-round effects dominate first-round effects, therefore suggesting that most current stress-test frameworks might lead to a severe underestimation of systemic risk.

Keywords: Systemic risk; leverage network; stress-test

MSC 2010: 91B30


  • [1]

    Acemoglu D., Ozdaglar A. and Tahbaz-Salehi A., Systemic risk and stability in financial networks, Amer. Econ. Rev. 105 (2015), no. 2, 564–608. Google Scholar

  • [2]

    Anand K., Craig B. and von Peter G., Filling in the blanks: Network structure and interbank contagion, Discussion Paper 2, Deutsche Bundesbank, 2014. Google Scholar

  • [3]

    Aoyama H., Battiston S. and Fujiwara Y., DebtRank analysis of the Japanese credit network, Discussion Paper 13-E-087, RIETI, 2013, www.rieti.go.jp/jp/publications/dp/13e087.pdf.

  • [4]

    Bank of England, A framework for stress testing the UK banking system, Technical Report October, Bank of England, 2013. Google Scholar

  • [5]

    Basel Committee on Banking Supervision, Basel III: A global regulatory framework for more resilient banks and banking systems, Bank for International Settlements, Basel, 2010. Google Scholar

  • [6]

    Basel Committee on Banking Supervision, Global systemically important banks: Assessment methodology and the additional loss absorbency requirement, Technical Report, Bank for International Settlements, 2011. Google Scholar

  • [7]

    Basel Committee on Banking Supervision, Liquidity stress testing: A survey of theory, empirics and current industry and supervisory practices, Bank for International Settlements, Basel, 2013. Google Scholar

  • [8]

    Basel Committee on Banking Supervision, Review of the credit valuation adjustment risk framework, Bank for International Settlements, Basel, 2015. Google Scholar

  • [9]

    Battiston S., Delli Gatti D., Gallegati M., Greenwald B. C. N. and Stiglitz J. E., Credit default cascades: When does risk diversification increase stability?, J. Financ. Stab. 8 (2012), no. 3, 138–149. Google Scholar

  • [10]

    Battiston S., Puliga M., Kaushik R., Tasca P. and Caldarelli G., DebtRank: Too central to fail? Financial networks, the Fed and systemic risk, Scientific Rep. 2 (2012), Paper No. 541. Google Scholar

  • [11]

    Beale N., Rand D. G., Battey H., Croxson K., May R. M. and Nowak M. A., Individual versus systemic risk and the regulator’s dilemma, Proc. Natl. Acad. Sci. USA 108 (2011), no. 31, 12647–12652. Google Scholar

  • [12]

    Bordo M., Mizrach B. and Schwartz A., Real versus pseudo-international systemic risk: Some lessons from history, Working Paper No. 5371, National Bureau of Economic Research, 1995. Google Scholar

  • [13]

    Borio C., Towards a macroprudential framework for financial supervision and regulation?, CESifo Econ. Stud. 49 (2003), no. 2, 181–215. Google Scholar

  • [14]

    Brock W. A., Hommes C. H. and Wagener F. O. O., More hedging instruments may destabilize markets, J. Econom. Dynam. Control 33 (2009), no. 11, 1912–1928. Google Scholar

  • [15]

    Caccioli F., Farmer J. D., Foti N. and Rockmore D., How interbank lending amplifies overlapping portfolio contagion, preprint 2013, https://arxiv.org/abs/1306.3704.

  • [16]

    Caldarelli G., Scale-Free Networks: Complex Webs in Nature and Technology, Oxford University Press, Oxford, 2007. Google Scholar

  • [17]

    Caldarelli G., Chessa A., Pammolli F., Gabrielli A. and Puliga M., Reconstructing a credit network, Nature Phys. 9 (2013), no. 3, 125–126. Google Scholar

  • [18]

    Cimini G., Squartini T., Gabrielli A. and Garlaschelli D., Estimating topological properties of weighted networks from limited information, Phys. Rev. E 92 (2015), 040802. Google Scholar

  • [19]

    Cimini G., Squartini T., Garlaschelli D. and Gabrielli A., Systemic risk analysis on reconstructed economic and financial networks, Scientific Reports 5 (2015), 10.1038/srep15758. Google Scholar

  • [20]

    Cont R., Moussa A. and Santos E. B., Network structure and systemic risk in banking systems, Handbook on Systemic Risk, Cambridge University Press, Cambridge (2013), 327–368. Google Scholar

  • [21]

    Cornell B., What moves stock prices: Another look, J. Portfolio Manag. 39 (2013), no. 3, 32–38. Google Scholar

  • [22]

    Crosbie P. and Bohn J., Modeling default risk, Working paper, KMV, 2003. Google Scholar

  • [23]

    Cutler D. M., Poterba J. M. and Summers L. H., What moves stock prices?, J. Portf. Manag. 15 (1989), no. 3, 4–12. Google Scholar

  • [24]

    Danielsson J., Shin H. S. and Zigrand J.-P., Endogenous and systemic risk, Quantifying Systemic Risk, University of Chicago Press, Chicago (2013), 73–94. Google Scholar

  • [25]

    de Masi G., Iori G. and Caldarelli G., Fitness model for the Italian interbank money market, Phys. Rev. E (3) 74 (2006), Article ID 066112. Google Scholar

  • [26]

    Di Iasio G., Battiston S., Infante L. and Pierobon F., Capital and contagion in financial networks, Paper No. 52141, University Library of Munich, Munich, 2013. Google Scholar

  • [27]

    Eisenberg L. and Noe T. H., Systemic risk in financial systems, Manag. Sci. 47 (2001), no. 2, 236–249. Google Scholar

  • [28]

    Elsinger H., Lehar A. and Summer M., Risk assessment for banking systems, Manag. Sci. 52 (2006), no. 9, 1301–1314.Google Scholar

  • [29]

    European Central Bank, ECB Comprehensive assessment, Technical report, 2014. Google Scholar

  • [30]

    Fink K., Krüger U., Meller B. and Wong L. H., Price interconnectedness, Discussion paper, Deutsche Bundesbank, 2014. Google Scholar

  • [31]

    Föllmer H. and Schied A., Stochastic Finance: An Introduction in Discrete Time, 3rd ed., De Gruyter, Berlin, 2011. Google Scholar

  • [32]

    Gai P., Haldane A. and Kapadia S., Complexity, concentration and contagion, J. Monetary Econ. 58 (2011), no. 5, 453–470. Google Scholar

  • [33]

    Geanakoplos J., Axtell R., Farmer D. J., Howitt P., Conlee B., Goldstein J., Hendrey M., Palmer N. M. and Yang C.-Y., Getting at systemic risk via an agent-based model of the housing market, Amer. Econ. Rev. 102 (2012), no. 3, 53–58. Google Scholar

  • [34]

    Glasserman P. and Peyton Young H., How likely is contagion in financial networks?, J. Banking Finance 50 (2015), 383–399. Google Scholar

  • [35]

    Hałaj G. and Kok C., Assessing interbank contagion using simulated networks, Comput. Manag. Sci. 10 (2013), no. 2–3, 157–186. Google Scholar

  • [36]

    Hałaj G. and Kok C., Modelling the emergence of the interbank networks, Quant. Finance 15 (2015), no. 4, 653–671. Google Scholar

  • [37]

    Huang X., Vodenska I., Havlin S. and Stanley H. E., Cascading failures in bi-partite graphs: Model for systemic risk propagation, Sci. Rep. 3 (2013), Paper No. 1219. Google Scholar

  • [38]

    Hurd T. R. and Gleeson J. P., A framework for analyzing contagion in banking networks, Social Sci. Res. Network 2011, http://dx.doi.org/10.2139/ssrn.1945748. Crossref

  • [39]

    in’t Veld D. and van Lelyveld I., Finding the core: Network structure in interbank markets, J. Banking Finance 49 (2014), 27–40. Google Scholar

  • [40]

    Iori G., Del Masi G., Precup O. V., Gabbi G. and Caldarelli G., A network analysis of the Italian overnight money market, J. Econom. Dynam. Control 32 (2008), no. 1, 259–278. Google Scholar

  • [41]

    Kolb R. W., Lessons from the Financial Crisis, John Wiley & Sons, Hoboken, 2010. Google Scholar

  • [42]

    Krugman P., Bergsten C. F., Dornbusch R., Frenkel J. A. and Kindleberger C. P., International aspects of financial crises, The Risk of Economic Crisis, University of Chicago Press, Chicago (1991), 85–134. Google Scholar

  • [43]

    Loepfe L., Cabrales A. and Sánchez A., Towards a proper assignment of systemic risk: The combined roles of network topology and shock characteristics, PlOS One 8 (2013), 10.1371/journal.pone.0077526. Google Scholar

  • [44]

    Markose S., Giansante S. and Shaghaghi A. R., Too interconnected to fail financial network of us cds market: Topological fragility and systemic risk, J. Econ. Behavior Org. 83 (2012), no. 3, 627–646. Google Scholar

  • [45]

    Martínez-Jaramillo S., Alexandrova-Kabadjova B., Bravo-Benítez B. and Solórzano Margain J. P., An empirical study of the mexican banking system’s network and its implications for systemic risk, J. Econom. Dynam. Control 40 (2012), 242–265. Google Scholar

  • [46]

    May R. M. and Arinaminpathy N., Systemic risk: The dynamics of model banking systems, J. Roy. Soc. Interface 7 (2010), no. 46, 823–838. Google Scholar

  • [47]

    McNeil A. J., Frey R. and Embrechts P., Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press, Princeton, 2010. Google Scholar

  • [48]

    Merton R. C., On the pricing of corporate debt: The risk structure of interest rates, J. Finance 29 (1974), no. 2, 449–470. Google Scholar

  • [49]

    Miranda R. and Tabak B., Contagion risk within firm-bank bivariate networks, Technical report, Central Bank of Brazil Research Department, 2013. Google Scholar

  • [50]

    Mistrulli P. E., Assessing financial contagion in the interbank market: Maximum entropy versus observed interbank lending patterns, J. Banking Finance 35 (2011), no. 5, 1114–1127. Google Scholar

  • [51]

    Montagna M. and Lux T., Contagion risk in the interbank market: A probabilistic approach to cope with incomplete structural information, Working Paper No. 1937, Kiel Institute for the World Economy, 2014. Google Scholar

  • [52]

    Musmeci N., Battiston S., Puliga M. and Gabrielli A., Bootstrapping topology and systemic risk of complex network using the fitness model, J. Stat. Phys. 151 (2013), no. 3–4, 720–734. Google Scholar

  • [53]

    Nier E., Yang J., Yorulmazer T. and Alentorn A., Network models and financial stability, J. Econom. Dynam. Control 31 (2007), no. 6, 2033–2060. Google Scholar

  • [54]

    Patzelt F. and Pawelzik K., An inherent instability of efficient markets, Sci. Rep. 3 (2013), Paper No. 2784. Google Scholar

  • [55]

    Poledna S. and Thurner S., Elimination of systemic risk in financial networks by means of a systemic risk transaction tax, preprint 2014, http://arxiv.org/abs/1401.8026.

  • [56]

    Puliga M., Caldarelli G. and Battiston S., Credit default swaps networks and systemic risk, Sci. Rep. 4 (2014), Paper No. 6822. Google Scholar

  • [57]

    Rogers L. C. G. and Veraart L. A. M., Failure and rescue in an interbank network, Manag. Sci. 59 (2013), no. 4, 882–898. Google Scholar

  • [58]

    Roukny T., Bersini H., Pirotte H., Caldarelli G. and Battiston S., Default cascades in complex networks: Topology and systemic risk, Sci. Rep. 3 (2013), Paper No. 2759. Google Scholar

  • [59]

    Roukny T., George C.-P. and Battiston S., A network analysis of the evolution of the German interbank market, Discussion Paper 22, Deutsche Bundesbank, 2014. Google Scholar

  • [60]

    Savage I. R. and Deutsch K. W., A statistical model of the gross analysis of transaction flows, Econometrica 28 (1960), no. 3, 551–572. Google Scholar

  • [61]

    Squartini T., van Lelyveld I. and Garlaschelli D., Early-warning signals of topological collapse in interbank networks, Sci. Rep. 3 (2013), Paper No. 3357. Google Scholar

  • [62]

    Stiglitz J. E., Risk and global economic architecture: Why full financial integration may be undesirable, Amer. Econ. Rev. 100 (2010), no. 2, 388–392.Google Scholar

  • [63]

    Tabak B. M., Souza S. R. S. and Guerra S. M., Assessing the systemic risk in the Brazilian interbank market, Working paper, Central Bank of Brazil, 2013. Google Scholar

  • [64]

    Tasca P. and Battiston S., Market procyclicality and systemic risk, Paper No. 45156, MPRA, 2013. Google Scholar

  • [65]

    Upper C. and Worms A., Estimating bilateral exposures in the German interbank market: Is there a danger of contagion?, Eur. Econ. Rev. 48 (2004), no. 4, 827–849. Google Scholar

About the article

Received: 2015-02-27

Revised: 2016-02-22

Accepted: 2016-07-26

Published Online: 2016-08-19

Published in Print: 2016-12-01

Funding Source: European Commission

Award identifier / Grant number: FET Open project SIMPOL nr. 610704

Award identifier / Grant number: FET Open DOLFINS nr. 640772

Award identifier / Grant number: ERC grant RMAC nr. 249415

SB and MD acknowledge support from the European Commission FET Open project SIMPOL nr. 610704, the European Commission FET Open DOLFINS nr. 640772, the European Commission ERC grant RMAC nr. 249415, and the Swiss National Science Foundation (SNF) Professorship grant no. PP00P1-144689.

Citation Information: Statistics & Risk Modeling, Volume 33, Issue 3-4, Pages 117–138, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1515/strm-2015-0005.

Export Citation

© 2016 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Daniel Grigat and Fabio Caccioli
Scientific Reports, 2017, Volume 7, Number 1
Stefano Battiston, Guido Caldarelli, Robert M. May, Tarik Roukny, and Joseph E. Stiglitz
Proceedings of the National Academy of Sciences, 2016, Volume 113, Number 36, Page 10031

Comments (0)

Please log in or register to comment.
Log in