IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v1y2001i6p641-649.html
   My bibliography  Save this article

Scaling in financial prices: IV. Multifractal concentration

Author

Listed:
  • B. B. Mandelbrot

Abstract

In the Brownian model, even the largest of N successive daily price increments contributes negligibly to the overall sample variance. The resulting 'absent' concentration justifies the role of variance in measuring Brownian volatility. Mandelbrot introduced in 1963 an alternative 'mesofractal model', in which the population variance is infinite. A significant proportion of the overall sample variance comes from an absolutely small number of large contributions, expressing a 'hard' form of concentration. To achieve a prescribed proportion of the overall measured variance, those 1900 and 1963 models require numbers of days of the order of N1 and N0, respectively. This paper shows that an intermediate possibility exists: a new and very flexible 'soft' form of concentration is provided by the 'multifractal' model Mandelbrot introduced in 1997. The standard 'extreme values' theory applies to mesofractals but multifractals behave very differently. The single largest contribution to sample variance is asymptotically negligible; however, an arbitrarily high proportion of the overall variance is contributed by a number of days of the order of ND, where 0

Suggested Citation

  • B. B. Mandelbrot, 2001. "Scaling in financial prices: IV. Multifractal concentration," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 641-649.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:6:p:641-649
    DOI: 10.1088/1469-7688/1/6/306
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1088/1469-7688/1/6/306
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1088/1469-7688/1/6/306?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. Wang, Yudong & Wu, Chongfeng & Yang, Li, 2016. "Forecasting crude oil market volatility: A Markov switching multifractal volatility approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 1-9.
    2. Sonali Agarwal & Anshul Vats, 2024. "A Comparative Study of Financial Crises: Fractal Dissection of Investor Rationality," Vision, , vol. 28(2), pages 193-209, April.
    3. Wilhelm Berghorn & Sascha Otto, 2017. "Mandelbrot Market-Model and Momentum," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 8(3), pages 1-26, July.
    4. Gencay, Ramazan & Selcuk, Faruk, 2004. "Extreme value theory and Value-at-Risk: Relative performance in emerging markets," International Journal of Forecasting, Elsevier, vol. 20(2), pages 287-303.
    5. Fieberg, Christian & Günther, Steffen & Poddig, Thorsten & Zaremba, Adam, 2024. "Non-standard errors in the cryptocurrency world," International Review of Financial Analysis, Elsevier, vol. 92(C).
    6. Sutthisit Jamdee & Cornelis A. Los, 2005. "Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate," Finance 0502021, University Library of Munich, Germany.
    7. M. A. H. Dempster, 2011. "Benoit B. Mandelbrot (1924-2010): a father of Quantitative Finance," Quantitative Finance, Taylor & Francis Journals, vol. 11(2), pages 155-156.
    8. Wilhelm Berghorn & Martin T. Schulz & Markus Vogl & Sascha Otto, 2021. "Trend Momentum II: Driving Forces of Low Volatility and Momentum," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 12(3), pages 300-319, May.
    9. Mehmet Ali Balcı & Larissa M. Batrancea & Ömer Akgüller & Lucian Gaban & Mircea-Iosif Rus & Horia Tulai, 2022. "Fractality of Borsa Istanbul during the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(14), pages 1-33, July.
    10. Chris Heyde, 2009. "Scaling issues for risky asset modelling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 593-603, July.

    More about this item

    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:taf:quantf:v:1:y:2001:i:6:p:641-649. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.