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Scaling in stock market data: stable laws and beyond


  • Rama Cont

    (CEA Saclay
    Science & Finance
    CNRS Nice)

  • Marc Potters

    (Science & Finance)

  • Jean-Philippe Bouchaud

    (CEA Saclay
    Science & Finance)


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.

Suggested Citation

  • Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Papers cond-mat/9705087,
  • Handle: RePEc:arx:papers:cond-mat/9705087

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    References listed on IDEAS

    1. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    2. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    3. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    4. Marc Potters & Rama Cont & Jean-Philippe Bouchaud, 1996. "Financial markets as adaptative systems," Science & Finance (CFM) working paper archive 500037, Science & Finance, Capital Fund Management.
    5. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Science & Finance (CFM) working paper archive 9705087, Science & Finance, Capital Fund Management.
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    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading


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