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Understanding the cubic and half-cubic laws of financial fluctuations

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

Abstract

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.

Suggested Citation

  • Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, H.Eugene, 2003. "Understanding the cubic and half-cubic laws of financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 1-5.
  • 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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    References listed on IDEAS

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    1. 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, arXiv.org.
    2. 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, arXiv.org.
    3. 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.
    4. 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.
    5. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    6. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    7. 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..
    8. 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, arXiv.org, revised May 1998.
    9. 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.
    10. 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.
    11. 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.
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    Cited by:

    1. Wei-Xing Zhou, 2007. "Universal price impact functions of individual trades in an order-driven market," Papers 0708.3198, arXiv.org, revised Apr 2008.
    2. Carlos León, 2014. "Scale-free tails in Colombian financial indexes: a primer," BORRADORES DE ECONOMIA 011144, BANCO DE LA REPÚBLICA.
    3. Huang, Jingjing & Shang, Pengjian & Zhao, Xiaojun, 2012. "Multifractal diffusion entropy analysis on stock volatility in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5739-5745.
    4. Gu, Gao-Feng & Zhou, Wei-Xing, 2007. "Statistical properties of daily ensemble variables in the Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 497-506.
    5. Eisenberg, Larry, 2011. "Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite," Journal of Financial Stability, Elsevier, vol. 7(1), pages 10-18, January.
    6. Gao-Feng Gu & Xiong Xiong & Yong-Jie Zhang & Wei Chen & Wei Zhang & Wei-Xing Zhou, 2014. "Stylized facts of price gaps in limit order books: Evidence from Chinese stocks," Papers 1405.1247, arXiv.org.
    7. Andrzej Krawiecki, 2009. "Microscopic spin model for the stock market with attractor bubbling on scale-free networks," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(2), pages 213-220, November.

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