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Understanding the cubic and half-cubic laws of financial fluctuations

  • Gabaix, Xavier
  • Gopikrishnan, Parameswaran
  • Plerou, Vasiliki
  • Stanley, H.Eugene

Recent empirical research has uncovered regularities in financial fluctuations. Those are: (i) the cubic law of returns: returns follow a power law distribution with exponent 3; (ii) the half cubic law of volumes: volumes follow a power law distribution with exponent 32; (iii) Approximate cubic law of number of trades: the number of trades in a given time intervals follows a power law distribution with exponent around 3. We discuss a new theory that explains them, as well as some related facts.

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Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 324 (2003)
Issue (Month): 1 ()
Pages: 1-5

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Handle: RePEc:eee:phsmap:v:324:y:2003:i:1:p:1-5
DOI: 10.1016/S0378-4371(03)00174-2
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  1. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113,
  2. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374,, revised May 1998.
  3. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305,
  4. Sorin Solomon & Peter Richmond, 2001. "Power Laws of Wealth, Market Order Volumes and Market Returns," Papers cond-mat/0102423,, revised Apr 2001.
  5. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
  6. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
  7. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
  8. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518,
  9. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161,
  10. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  11. Maslov, Sergei & Mills, Mark, 2001. "Price fluctuations from the order book perspective—empirical facts and a simple model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 234-246.
  12. Gopikrishnan, P. & Plerou, V. & Gabaix, X. & Amaral, L.A.N. & Stanley, H.E., 2001. "Price fluctuations and market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 137-143.
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