The European Physical Journal B

, Volume 67, Issue 3, pp 399–417 | Cite as

Minimal agent based model for financial markets II

Statistical properties of the linear and multiplicative dynamics
  • V. Alfi
  • M. Cristelli
  • L. Pietronero
  • A. Zaccaria
Interdisciplinary Physics Regular Article


We present a detailed study of the statistical properties of the Agent Based Model introduced in paper I [Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4] and of its generalization to the multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the stylized facts and their self-organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. We consider a linear approximation for the price dynamics which permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and self-organization of the stylized facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the stylized facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.


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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4Google Scholar
  2. T. Lux, M. Marchesi, Nature 397, 498 (1999)Google Scholar
  3. T. Lux, M. Marchesi, International Journal of Theoretical and Applied Finance 3, 675 (2000)Google Scholar
  4. E. Samanidou, E. Zschischang, D. Stauffer, T. Lux, Rep. Prog. Phys. 70, 409 (2007)Google Scholar
  5. C.H. Hommes, in Handbook of Computational Economics, edited by K.L. Judd, L.S. Tesfatsion (North-Holland Elsevier, Amsterdam, 2006)Google Scholar
  6. B. LeBaron, in Handbook of Computational Economics, edited by K.L. Judd, L.S. Tesfatsion (North-Holland Elsevier, Amsterdam, 2006)Google Scholar
  7. V. Alfi, L. Pietronero, A. Zaccaria, e-print arXiv:0807.1888 (2008)Google Scholar
  8. G. Grimmett, D. Stirzaker, Probability and random processes (Oxford University Press, Oxford, 2004)Google Scholar
  9. M. Takayasu, T. Mizuno, H. Takayasu, Physica A 370, 91 (2006)Google Scholar
  10. T. Mizuno, H. Takayasu, M. Takayasu, Physica A 382, 187 (2007)Google Scholar
  11. I.I. Gihman, A.V. Skorohod, The theory of stochastic processes (Springer-Verlag, New York, Heidelberg, Berlin, 1974)Google Scholar
  12. R. Cont, Quant. Finance 1, 223 (2001)Google Scholar
  13. B. LeBaron, in Medium Econometrische Toepassingen (MET) (Erasmus University, 2006)Google Scholar
  14. M. Kreps, A Course in Microeconomic Theory (Princeton University Press, 1990)Google Scholar
  15. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlation and Complexity in Finance (Cambridge University Press, New York, NY, USA, 2000)Google Scholar
  16. J.P. Bouchaud, M. Potters, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management (Cambridge University Press, 2003)Google Scholar
  17. A. Joulin, A. Lefevre, D. Grunberg, J.-P. Bouchaud, e-print arXiv:0803.1769 Google Scholar
  18. S. Mike, J.D. Farmer, J. Economic Dynamics and Control 32, 200 (2008)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

Personalised recommendations