The European Physical Journal B

, Volume 67, Issue 3, pp 385–397 | Cite as

Minimal agent based model for financial markets I

Origin and self-organization of stylized facts
Interdisciplinary Physics Regular Article

Abstract

We introduce a minimal agent based model for financial markets to understand the nature and self-organization of the stylized facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the most important deviations of price time series from a random walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The stylized facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effects which, however, can occur at different time scales. We propose a new mechanism for the self-organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represents a crucial element for this state of self-organized intermittency. The model can be easily generalized to consider more realistic variants.

PACS

89.65.Gh Economics; econophysics, financial markets, business and management 89.75.-k Complex systems 

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References

  1. L. Bachelier, Ph.D. thesis, Annales Scientifiques de l’École Normale Supérieure (1900)Google Scholar
  2. R. Cont, Quant. Finance 1, 223 (2001)Google Scholar
  3. R.N. Mantegna, H. Stanley, An Introduction to Econophysics: Correlation and Complexity in Finance (Cambridge University Press, New York, NY, USA, 2000)Google Scholar
  4. J.P. Bouchaud, M. Potters, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management (Cambridge University Press, 2003)Google Scholar
  5. B. Mandelbrot, J. Business 36, 394 (1963)Google Scholar
  6. B. Mandelbrot, Fractals and Scaling in Finance (Springer Verlag, New York, 1997)Google Scholar
  7. R. Engle, Econometrica 50, 987 (1982)Google Scholar
  8. C. Tsallis, C. Anteneodo, L. Borland, R. Osorio, Physica A 324, 89 (2003)Google Scholar
  9. L. Borland, Phys. Rev. Lett. 89, 098701 (2002)Google Scholar
  10. F. Baldovin, A. Stella, PNAS 104, 19741 (2007)Google Scholar
  11. B. LeBaron, in Medium Econometrische Toepassingen (MET) (Erasmus University, 2006)Google Scholar
  12. V. Alfi, L. Pietronero, A. Zaccaria, e-print arXiv:0807.1888 (2008)Google Scholar
  13. V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00029-3Google Scholar
  14. T. Lux, M. Marchesi, Nature 397, 498 (1999)Google Scholar
  15. T. Lux, M. Marchesi, International Journal of Theoretical and Applied Finance 3, 675 (2000)Google Scholar
  16. G. Vaglica, F. Lillo, E. Moro, N. Mantegna, Phys. Rev. E 77, 036110 (2008)Google Scholar
  17. M. Takayasu, T. Mizuno, H. Takayasu, Physica A 370, 91 (2006)Google Scholar
  18. T. Mizuno, H. Takayasu, M. Takayasu, Physica A 382, 187 (2007)Google Scholar
  19. V. Alfi, F. Coccetti, M. Marotta, L. Pietronero, M. Takayasu, Physica A 370, 30 (2006)Google Scholar
  20. V. Alfi, A. De Martino, A. Tedeschi, L. Pietronero, Physica A 382, 1 (2007)Google Scholar
  21. A. Kirman, Quart. J. Econ. 180, 137 (1993)Google Scholar
  22. M. Kreps, A Course in Microeconomic Theory (Princeton University Press, 1990)Google Scholar
  23. S. Alfarano, T. Lux, F. Wagner, Journal of Economic Dynamics & Control 32, 101 (2008)Google Scholar
  24. S. Alfarano, T. Lux, F. Wagner, Comput. Econ. 26, 19 (2005)Google Scholar
  25. C. Gardiner, Handbook of stochastic methods: for physics, chemistry and the natural sciences (Springer, Berlin, 1990)Google Scholar
  26. E. Egenter, T. Lux, D. Stauffer, Physica A 268, 250 (1999)Google Scholar
  27. T. Bollerslev, J. Econometrics 31, 307 (1986)Google Scholar
  28. T.A. Witten, L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)Google Scholar
  29. L. Niemeyer, L. Pietronero, H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)Google Scholar
  30. P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)Google Scholar
  31. H. Jensen, Self-organized criticality (Cambridge University Press, Cambridge, 1998)Google Scholar
  32. P. Bak, How Nature Works: The Science of Self-Organised Criticality (Copernicus Press, New York, 1996)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • V. Alfi
    • 1
    • 2
  • M. Cristelli
    • 1
  • L. Pietronero
    • 1
    • 3
  • A. Zaccaria
    • 1
  1. 1.Università “La Sapienza”RomaItaly
  2. 2.Centro “E. Fermi”, Compendio ViminaleRomaItaly
  3. 3.ISC-CNR, V. dei Taurini 19RomaItaly

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