Advanced Search
MyIDEAS: Login to save this paper or follow this series

The statistical properties of the volatility of price fluctuations

Contents:

Author Info

  • Yanhui Liu
  • Parameswaran Gopikrishnan
  • Pierre Cizeau
  • Martin Meyer
  • Chung-Kang Peng
  • H. Eugene Stanley
Registered author(s):

    Abstract

    We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the 13-year period Jan 1984 to Dec 1996 and (b) the market capitalizations of the largest 500 companies registered in the Trades and Quotes data base, documenting all trades for all the securities listed in the three major stock exchanges in the US for the 2-year period Jan 1994 to Dec 1995. For the S&P 500 index, the probability density function of the volatility can be fit with a log-normal form in the center. However, the asymptotic behavior is better described by a power-law distribution characterized by an exponent 1 + \mu \approx 4. For individual companies, we find a power law asymptotic behavior of the probability distribution of volatility with exponent 1 + \mu \approx 4, similar to the S&P 500 index. In addition, we find that the volatility distribution scales for a range of time intervals. Further, we study the correlation function of the volatility and find power law decay with long persistence for the S&P 500 index and the individual companies with a crossover at approximately 1.5 days. To quantify the power-law correlations, we apply power spectrum analysis and a recently-developed modified root-mean-square analysis, termed detrended fluctuation analysis (DFA). For the S&P 500 index, DFA estimates for the exponents characterizing the power law correlations are \alpha_1=0.66 for short time scales (within \approx 1.5 days) and \alpha_2=0.93 for longer time scales (up to a year). For individual companies, we find \alpha_1=0.60 and \alpha_2=0.74, respectively. The power spectrum gives consistent estimates of the two power-law exponents.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://arxiv.org/pdf/cond-mat/9903369
    File Function: Latest version
    Download Restriction: no

    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/9903369.

    as in new window
    Length:
    Date of creation: Mar 1999
    Date of revision: Mar 1999
    Publication status: Published in Phys. Rev. E 60 (1999) 1390
    Handle: RePEc:arx:papers:cond-mat/9903369

    Contact details of provider:
    Web page: http://arxiv.org/

    Related research

    Keywords:

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as in new window

    Cited by:
    This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/9903369. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.