The dynamics of financial stability in complex networks

  • J. P. da CruzEmail author
  • P. G. Lind
Regular Article


We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange ‘economic energy’, forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability.


Statistical and Nonlinear Physics 


  1. 1.
    Basel Committee on Banking Supervision,International convergence of capital measurement and capital standards (1998),
  2. 2.
    Basel Committee on Banking Supervision,Basel ii: International convergence of capital measurement and capital standards: a revised framework (2004),
  3. 3.
    O. Vasicek,Probability of loss on loan portfolio(KMV Corporation, 1987),
  4. 4.
    R. Frey, A. McNeil, J. Bank. Financ. 26, 1317 (2002)CrossRefGoogle Scholar
  5. 5.
    Basel Committee on Banking Supervision,International regulatory framework for banks (basel iii) (2010),
  6. 6.
    J. Daníelsson, P. Embrechts, C. Goodhart, C. Keating, F. Muennich, O. Renault, H. Song Shin, An academic response to basel ii (2001),
  7. 7.
    L. Borland, J.P. Bouchaud, J.F. Muzy, G. Zumbach,The dynamics of financial markets – mandelbrot’s multifractal cascades, and beyond(Wilmott Magazine, 2005)Google Scholar
  8. 8.
    J.P. Bouchaud, M. Potters,Theory of Financial Risk and Derivative Pricing From Statistical Physics to Risk Management (Cambridge University Press, Cambridge, 2003)Google Scholar
  9. 9.
    B. Mandelbrot, R. Hudson,The (mis)Behavior of Markets – A Fractal View of Risk, Ruin, and Reward(Basic Books, USA, 2004)Google Scholar
  10. 10.
    D. Sornette,Why Stock Markets Crash?(Princeton University Press, 2003)Google Scholar
  11. 11.
    P. Embrechts, C. Kluppelberg, T. Mikosch,Modelling Extreme Events in Insurance and Finance(Springer-Verlag, 1997)Google Scholar
  12. 12.
    R.N. Mantegna, H.E. Stanley, Phys. Rev. Lett. 73, 2946 (1994)MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, Y. Dodge, Nature 381, 767 (1996)ADSCrossRefGoogle Scholar
  14. 14.
    E. Samanidou, E. Zschischang, D. Stauffer, T. Lux.Rep. Prog. Phys 70, 409 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)ADSCrossRefGoogle Scholar
  16. 16.
    T. Wenzel,Beyond GDP: Measuring the Wealth of Nations (GRIN, 2009)Google Scholar
  17. 17.
    R. Lipsey, P. Steyner,Economics(Harper & Row, USA, 1981)Google Scholar
  18. 18.
    J.P. da Cruz, P.G. Lind, Physica A 391, 1445 (2012)ADSGoogle Scholar
  19. 19.
    S.N.D. Queirós, E.M.F. Curado, F.D. Nobre, Physica A 374, 715 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    V. Plerou, P. Gopikrishnan, X. Gabaix, H.E. Stanley, Phys. Rev. E 66, 027104 (2002)ADSGoogle Scholar
  21. 21.
    S.A. Ross, R.W. Westerfield, J.F. Jaffe, Corporate Finance, 6th edn. (McGrawHill, 2003)Google Scholar
  22. 22.
    IFRS Foundation,International financial reporting standards (2011),
  23. 23.
    R.C. Merton, J. Financ. 29, 449 (1974)Google Scholar
  24. 24.
    A.-L. Barabási, R. Albert, Science 286, 509 (1999)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    M.-B. Hu, W.-X. Wang, R. Jiang, Q.-S. Wu, B.-H. Wang, Y.-H. Wu, Eur. Phys. J. B 53, 273 (2006)ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    V. Pareto, Le Cours d’Economique Politique (Macmillan, Lausanne, Paris, 1897)Google Scholar
  27. 27.
    J.P. da Cruz, P.G. Lind, Bounding heavy-tailed return distributions to measure model risk (2011),
  28. 28.
    M. Defond, C. Lennox, The effect of sox on small auditor exits and audit quality, in Singapore Management University (SMU) Accounting Symposium Google Scholar
  29. 29.
    P. Erdös, A. Rényi, Publ. Math. (Debrecen) 6, 290 (1959)MathSciNetzbMATHGoogle Scholar
  30. 30.
    R. Piazza, Growth and crisis, unavoidable connection? (2010),
  31. 31.
    A.G. Haldane, R.M. May, Nature 469, 351 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    G. Iori, S. Jafarey, F. Padilla, J. Econ. Behav. Organ. 61, 525 (2006)CrossRefGoogle Scholar
  33. 33.
    European Commission, IMF, ECB, Portugal: Memorandum of understanding (mou) on specific economic policy conditionality (2011)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Departamento de FísicaFaculdade de Ciências da Universidade de LisboaLisboaPortugal
  2. 2.Closer Consultoria Lda, Avenida Engenheiro Duarte PachecoLisboaPortugal
  3. 3.Center for Theoretical and Computational PhysicsUniversity of LisbonLisbonPortugal

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