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Power-laws in economics and finance: some ideas from physics

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  • Jean-Philippe Bouchaud

    (Science & Finance, Capital Fund Management
    CEA Saclay;)

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    Abstract

    We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments distribution and the decay of the volatility correlations are rather robust and suggest universality. However, many of the models that appear naturally (for example, to account for the distribution of wealth) contain some multiplicative noise, which generically leads to *non universal exponents*. Recent progress in the empirical study of the volatility suggests that the volatility results from some sort of multiplicative cascade. A convincing `microscopic' (i.e. trader based) model that explains this observation is however not yet available. It would be particularly important to understand the relevance of the pseudo-geometric progression of natural human time scales on the long range nature of the volatility correlations.

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    Bibliographic Info

    Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500023.

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    Date of creation: Aug 2000
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    Publication status: Published in Quantitative Finance, proccedings of the 2000 Santa Fe conference
    Handle: RePEc:sfi:sfiwpa:500023

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    References

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    1. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October.
    2. J. Doyne Farmer, 1998. "Market Force, Ecology, and Evolution," Research in Economics 98-12-117e, Santa Fe Institute.
    3. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Papers cond-mat/9705087, arXiv.org.
    4. J. Doyne Farmer, 1999. "Physicists Attempt to Scale the Ivory Towers of Finance," Working Papers 99-10-073, Santa Fe Institute.
    5. Irene Giardina & Jean-Philippe Bouchaud & Marc Mezard, 2000. "Population dynamics in a random environment," Science & Finance (CFM) working paper archive 500025, Science & Finance, Capital Fund Management.
    6. Hideaki Aoyama & Yuichi Nagahara & Mitsuhiro P. Okazaki & Wataru Souma & Hideki Takayasu & Misako Takayasu, 2000. "Pareto's Law for Income of Individuals and Debt of Bankrupt Companies," Papers cond-mat/0006038, arXiv.org.
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    Cited by:
    1. Jean Pierre Nadal & Denis Phan & Mirta B. Gordan & Jean Vannimenus, 2003. "Monopoly Market with Externality: an Analysis with Statistical Physics and ACE," Computational Economics 0312002, EconWPA.
    2. Jean-Pierre Nadal & Denis Phan & Mirta B. Gordon & Jean Vannimenus, 2003. "Monopoly Market with Externality: an Analysis with Statistical Physics and Agent Based Computational Economics," Papers cond-mat/0311096, arXiv.org.
    3. Jean-Pierre Nadal & Denis Phan & Mirta Gordon & Jean Vannimenus, 2005. "Multiple equilibria in a monopoly market with heterogeneous agents and externalities," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 557-568.
    4. Denis Phan & Stephane Pajot & Jean-Pierre Nadal, 2003. "The Monopolist's Market with Discrete Choices and Network Externality Revisited: Small-Worlds, Phase Transition and Avalanches in an ACE Framework," Computing in Economics and Finance 2003 150, Society for Computational Economics.

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