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Clearing Algorithms and Network Centrality

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Complex Networks and Their Applications VII (COMPLEX NETWORKS 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 813))

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Abstract

I show that the solution of a standard clearing model commonly used in contagion analyses for financial systems can be expressed as a specific form of a generalized Katz centrality measure under conditions that correspond to a system-wide shock. This result provides a formal explanation for earlier empirical results which showed that Katz-type centrality measures are closely related to contagiousness. It also allows assessing the assumptions that one is making when using such centrality measures as systemic risk indicators. I conclude that these assumptions should be considered too strong and that, from a theoretical perspective, clearing models should be given preference over centrality measures in systemic risk analyses.

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Notes

  1. 1.

    Note that by setting \(D_{NN}=1\) for the sink node, I am assuming that this node makes payments even though it has no liabilities. This has no implication for the solutions for the other banks, as these payments do not arrive anywhere. Given that the sink node does not need to make payments within the system (and can generally not be interpreted as an entity with a balance sheet), its value for the clearing payment vector can safely be ignored. Other authors (see e.g. [17]) choose to exclude the sink node entirely, in this application, however, it is needed for calculation purposes, in the manner introduced here, as we shall see later.

  2. 2.

    The conditions define that certain subsets of the financial system need to have a positive value of external assets. I will use \(a_i>0 \forall i\) as a sufficient condition.

  3. 3.

    Note that the inclusion of a sink node is crucial here, as [8] show that for \(a_i>0 \forall i\) not all nodes can be in fundamental default. In this setup, it is the sink node that has positive equity value, but is still considered to be in default under any D(x) by construction.

  4. 4.

    In order to find suitable values for s, the model has to be solved first. Given that the aim is to have a small shock size, a reasonable approach would be to start by setting \(s_i = (-o_i + l_i - (Cl)_i)) - \frac{k}{MaxSteps} (l_i - (Cl)_i)\) for a suitable \(MaxSteps = 1000\), e.g., and iterating over \(k = 1, 2, \dots \) until \(D(p) = I\).

  5. 5.

    Another shortcoming of the \(\sigma \)-measure is that differences in initial capitalization, which are a significant driver of contagion dynamics, are canceled out through the shock. If one wanted to use the \(\sigma \) measure for systemic risk analysis, one should consider including another factor like \(\frac{s_i}{o_i + (Cl)_i}\) to capture the initial financial health of firm i.

References

  1. Acemoglu, D., Ozdaglar, A., Tahbaz-Salehi, A.: Systemic risk and stability in financial networks. Am. Econ. Rev. 105(2), 564–608 (2015). https://doi.org/10.1257/aer.20130456

    Article  Google Scholar 

  2. Allen, F., Gale, D.: Financial contagion. J. Polit. Econ. 108(1), 1–33 (2000)

    Article  Google Scholar 

  3. Alter, A., Craig, B., Raupach, P.: Centrality-based capital allocations and bailout. Int. J. Cent. Bank. 11(3), 329–379 (2015)

    Google Scholar 

  4. Anand, K., Craig, B., Von Peter, G.: Filling in the blanks: network structure and interbank contagion. Quant. Financ. 15(4), 625–636 (2015). https://doi.org/10.1080/14697688.2014.968195; http://www.bis.org/publ/work455.htm

  5. Barucca, P., Bardoscia, M., Caccioli, F., D ’errico, M., Visentin, G., Battiston, S., Caldarelli, G.: Network valuation in financial systems. In: SSRN Working Paper (2016)

    Google Scholar 

  6. Battiston, S., Puliga, M., Kaushik, R., Tasca, P., Caldarelli, G.: DebtRank: too central to fail? Financial networks, the FED and systemic risk. Sci. Rep. 2(541) (2012). https://doi.org/10.1038/srep00541; http://www.nature.com/srep/2012/120802/srep00541/full/srep00541.html

  7. Boss, M., Elsinger, H., Summer, M., Thurner, S.: The network topology of the interbank market. Quant. Financ. 4(6), 677–684 (2004). https://doi.org/10.1080/14697680400020325; http://arxiv.org/abs/cond-mat/0309582

  8. Eisenberg, L., Noe, T.H.: Risk in financial systems. Manag. Sci. 47(2), 236–249 (2001)

    Article  Google Scholar 

  9. Elsinger, H.: Financial networks, cross holdings and limited liability. OeNB Working Paper Series (2009)

    Google Scholar 

  10. Elsinger, H., Lehar, A., Summer, M.: Risk assessment for banking systems. Manag. Sci. 52(9), 1301–1314 (2006)

    Article  Google Scholar 

  11. Elsinger, H., Lehar, A., Summer, M.: Network models and systemic risk assessment (2012)

    Google Scholar 

  12. Fischer, T.: No-arbitrage pricing under systemic risk: accounting for cross-ownership. Math. Financ. 24(1), 97–124 (2014). https://doi.org/10.1111/j.1467-9965.2012.00526.x

    Article  MathSciNet  MATH  Google Scholar 

  13. Freixas, X., Parigi, B., Rochet, J.: Systemic risk, interbank relations, and liquidity provision by the central bank. J. Money Credit Bank. 32(3(2)), 611–638 (2000)

    Article  Google Scholar 

  14. Fukker, G.: Harmonic distances and systemic stability in heterogeneous interbank networks. Magyar Nemzeti Bank Working Papers (1) (2017)

    Google Scholar 

  15. Furfine, C.H.: Interbank exposures: quantifying the risk of contagion. J. Money Credit Bank. 35(1), 111–128 (2003). https://doi.org/10.2307/3649847; http://www.jstor.org/stable/3649847

  16. Gauthier, C., Gravelle, T., Liu, X.: What matters in determining capital surcharge for systemically important financial institutions? Simulation in computational finance and economics: tools and emerging applications. In: IGI Global pp. 211–224 (2013). http://www.igi-global.com/chapter/matters-determining-capital-surcharge-systemically/68698

  17. Glasserman, P., Young, H.P.: Contagion in financial networks. J. Econ. Lit. 54(3), 779–831 (2016). https://doi.org/10.1257/jel.20151228; http://pubs.aeaweb.org/doi/10.1257/jel.20151228

  18. Iori, G., Jafarey, S., Padilla, F.G.: Systemic risk on the interbank market. J. Econ. Behav. Organ. 61(4), 525–542 (2006). https://doi.org/10.1016/j.jebo.2004.07.018; http://linkinghub.elsevier.com/retrieve/pii/S0167268106001417

  19. Katz, L.: A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)

    Article  MathSciNet  Google Scholar 

  20. Kiyotaki, N., Moore, J.: Balance-sheet contagion. Am. Econ. Rev. 92(2), 46–50 (2002)

    Google Scholar 

  21. Kobayashi, T.: Network versus portfolio structure in financial systems. Eur. Phys. J. B 86(434) (2013). https://doi.org/10.1140/epjb/e2013-40072-9

  22. Kuzubaş, T.U., Ömercikoğlu, I., Saltoğlu, B.: Network centrality measures and systemic risk: an application to the Turkish financial crisis. Phys. A: Stat. Mech. Appl. 405, 203–215 (2014). https://doi.org/10.1016/j.physa.2014.03.006; http://www.sciencedirect.com/science/article/pii/S0378437114002003

  23. Merton, R.: On the pricing of corporate debt: the risk structure of interest rates*. J. Financ. (1974). http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1974.tb03058.x/full

  24. Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010). https://global.oup.com/academic/product/networks-9780199206650?cc=gb&lang=en&

  25. Nier, E., Yang, J., Yorulmazer, T., Alentorn, A.: Network models and financial stability. J. Econ. Dyn. Control. 31(6), 2033–2060 (2007). https://doi.org/10.1016/j.jedc.2007.01.014

    Article  MATH  Google Scholar 

  26. Puhr, C., Seliger, R., Sigmund, M.: Contagiousness and vulnerability in the Austrian interbank market. In: SSRN Working Paper (2014). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2442711

  27. Rochet, J., Tirole, J.: Interbank lending and systemic risk. J. Money Credit Bank. 28(4), 733–762 (1996)

    Article  Google Scholar 

  28. Rogers, L., Veraart, L.A.M.: Faliure and rescue in an interbank network. Manag. Sci. 59(4), 882–898 (2013). https://doi.org/10.1287/mnsc.1120.1569; http://www.informs.org/Pubs/ManSci

  29. Suzuki, T.: Valuing corporate debt: the effect of cross-holdings of stock and debt. J. Oper. Res. Soc. Jpn. 45(2), 123–144 (2002)

    Article  MathSciNet  Google Scholar 

  30. Tahbaz-Salehi, A.: Discussion of “centrality-based capital allocations”. Int. J. Cent. Bank. 11(3), 379–385 (2015)

    Google Scholar 

  31. Upper, C.: Simulation methods to assess the danger of contagion in interbank markets. J. Financ. Stab. 7(3), 111–125 (2011). https://doi.org/10.1016/j.jfs.2010.12.001; http://linkinghub.elsevier.com/retrieve/pii/S1572308910000550

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Authors and Affiliations

  1. University of Oxford, Mathematical Institute, Oxford, OX2 6GG, UK

    Christoph Siebenbrunner

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  1. Christoph Siebenbrunner
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Correspondence to Christoph Siebenbrunner .

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Editors and Affiliations

  1. Nokia Bell Labs, Cambridge, UK

    Luca Maria Aiello

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I UMR CNRS 6306 9, University of Burgundy, Dijon Cedex, France

    Hocine Cherifi

  4. Mathematical Institute, University of Oxford, Oxford, UK

    Renaud Lambiotte

  5. Department of Computer Science and Technology, The Computer Laboratory, University of Cambridge, Cambridge, UK

    Pietro Lió

  6. Center for Complex Networks and Systems Research, School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis M. Rocha

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Siebenbrunner, C. (2019). Clearing Algorithms and Network Centrality. In: Aiello, L., Cherifi, C., Cherifi, H., Lambiotte, R., Lió, P., Rocha, L. (eds) Complex Networks and Their Applications VII. COMPLEX NETWORKS 2018. Studies in Computational Intelligence, vol 813. Springer, Cham. https://doi.org/10.1007/978-3-030-05414-4_40

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