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Scaling in stock market data: stable laws and beyond

  • Rama Cont

    (Science & Finance, Capital Fund Management)

  • Marc Potters

    (Science & Finance, Capital Fund Management)

  • Jean-Philippe Bouchaud

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

The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications to market data we indicate the shortcomings of such models and describe the truncated Levy flight as an alternative model for price movements. Furthermore, studying the dependence structure of the price increments shows that while their autocorrelation function decreases rapidly to zero, the correlation of their squares and absolute values shows a slow power law decay, indicating persistence in the scale of fluctuations, a property which can be related to the anomalous scaling of the kurtosis. In the last section we review, in the light of these empirical facts, recent attempts to draw analogies between scaling in financial markets and in turbulent flows.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 9705087.

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Date of creation: May 1997
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Publication status: Published in `Scale Invariance and Beyond' (proceedings of the CNRS Workshop on Scale Invariance, Les Houches, March 1997) EDP-Springer
Handle: RePEc:sfi:sfiwpa:9705087
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