IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v92y2019i3d10.1140_epjb_e2019-90218-8.html
   My bibliography  Save this article

Distributions of historic market data – stock returns

Author

Listed:
  • Zhiyuan Liu

    (University of Cincinnati)

  • M. Dashti Moghaddam

    (University of Cincinnati)

  • R. A. Serota

    (University of Cincinnati)

Abstract

We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that the mean realized variance of returns is a linear function of the number of days over which the returns are calculated. The slope is determined by the mean value of the variance (squared volatility) in the mean-reverting stochastic volatility models, such as Heston and multiplicative, independent of stochasticity. The distribution function of stock returns, which rescales with the increase of the number of days of return, is obtained from the steady-state variance distribution function using the product distribution with the normal distribution. Graphical abstract

Suggested Citation

  • Zhiyuan Liu & M. Dashti Moghaddam & R. A. Serota, 2019. "Distributions of historic market data – stock returns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(3), pages 1-10, March.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:3:d:10.1140_epjb_e2019-90218-8
    DOI: 10.1140/epjb/e2019-90218-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/e2019-90218-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/e2019-90218-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distributions of Historic Market Data -- Relaxation and Correlations," Papers 1907.05348, arXiv.org, revised Feb 2020.
    2. Jiong Liu & M. Dashti Moghaddam & R. A. Serota, 2023. "Are there Dragon Kings in the Stock Market?," Papers 2307.03693, arXiv.org.

    More about this item

    Keywords

    Statistical and Nonlinear Physics;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:92:y:2019:i:3:d:10.1140_epjb_e2019-90218-8. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.