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Criticality and finite size effects in a simple realistic model of stock market

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  • Damien Challet
  • Matteo Marsili

Abstract

We discuss a simple model based on the Minority Game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit and show that stylized facts arise only close to a line of critical points with non-trivial properties. By a simple argument, we show that, in Minority Games, the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets as critical systems.

Suggested Citation

  • Damien Challet & Matteo Marsili, 2002. "Criticality and finite size effects in a simple realistic model of stock market," Papers cond-mat/0210549, arXiv.org, revised Dec 2002.
  • Handle: RePEc:arx:papers:cond-mat/0210549
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    Cited by:

    1. Lux, Thomas & Schornstein, Sascha, 2005. "Genetic learning as an explanation of stylized facts of foreign exchange markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 169-196, February.
    2. Andre Cardoso Barato & Iacopo Mastromatteo & Marco Bardoscia & Matteo Marsili, 2011. "Impact of meta-order in the Minority Game," Papers 1112.3908, arXiv.org, revised Nov 2012.
    3. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulation Framework for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org.
    4. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
    5. Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005. "Evolutionary dynamics in markets with many trader types," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 7-42, February.
    6. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    7. Goldbaum, David, 2006. "Self-organization and the persistence of noise in financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1837-1855.

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