IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v19y2008i03ns012918310801225x.html
   My bibliography  Save this article

Fractional Market Model And Its Verification On The Warsaw Stock Exchange

Author

Listed:
  • MARZENA KOZŁOWSKA

    (Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University, Smyczkowa Str. 5/7, PL-02678 Warsaw, Poland)

  • ANDRZEJ KASPRZAK

    (Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University, Smyczkowa Str. 5/7, PL-02678 Warsaw, Poland)

  • RYSZARD KUTNER

    (Division of Physics Education, Institute of Experimental Physics, Department of Physics, Warsaw University, Smyczkowa Str. 5/7, PL-02678 Warsaw, Poland)

Abstract

We analyzed the rising and relaxation of thecusp-like local peaks superposed with oscillations which were well defined by the Warsaw Stock Exchange index WIG in a daily time horizon. We found that the falling paths of all index peaks were described by a generalized exponential function or the Mittag-Leffler (ML) one superposed with various types of oscillations.However, the rising paths (except the first one of WIG which rises exponentially and the most important last one which rises again according to the ML function) can be better described by bullish anti-bubbles or inverted bubbles.2–4The ML function superposed with oscillations is a solution of the nonhomogeneous fractional relaxation equation which defines here our Fractional Market Model (FMM) of index dynamics which can be also called the Rheological Model of Market. This solution is a generalized analog of an exactly solvable fractional version of the Standard or Zener Solid Model of viscoelastic materials commonly used in modern rheology.5For example, we found that the falling paths of the index can be considered to be a system in the intermediate state lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlrausch-Williams-Watts (KWW) law for the initial times, and the power-law or the Nutting law for asymptotic time. Some rising paths (i.e., the bullish anti-bubbles) are a kind of log-periodic oscillations of the market in the bullish state initiated by a crash. The peaks of the index can be viewed as precritical or precrash ones since:(i) the financial market changes its state too early from the bullish to bearish one before it reaches a scaling region (defined by the diverging power-law of return per unit time), and(ii) they are affected by a finite size effect.These features could be a reminiscence of a significant risk aversion of the investors and their finite number, respectively. However, this means that the scaling region (where the relaxations of indexes are described by the KWW law or stretched exponential decay) was not observed. Hence, neither was the power-law of the instantaneous returns per unit time observed. Nevertheless, criticality or crash is in a natural way contained in our FMM and we found its "finger print".

Suggested Citation

  • Marzena Kozłowska & Andrzej Kasprzak & Ryszard Kutner, 2008. "Fractional Market Model And Its Verification On The Warsaw Stock Exchange," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 453-469.
  • Handle: RePEc:wsi:ijmpcx:v:19:y:2008:i:03:n:s012918310801225x
    DOI: 10.1142/S012918310801225X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S012918310801225X
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S012918310801225X?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.

    References listed on IDEAS

    as
    1. Roehner,Bertrand M., 2002. "Patterns of Speculation," Cambridge Books, Cambridge University Press, number 9780521802635, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Kozłowska, M. & Denys, M. & Wiliński, M. & Link, G. & Gubiec, T. & Werner, T.R. & Kutner, R. & Struzik, Z.R., 2016. "Dynamic bifurcations on financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 126-142.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter Richmond & Bertrand M. Roehner, 2016. "Property bubble in Hong Kong: A predicted decade-long slump (2016-2025)," Papers 1608.03985, arXiv.org.
    2. Geoffrey Poitras & John Heaney, 2015. "Classical Ergodicity and Modern Portfolio Theory," Post-Print hal-03680380, HAL.
    3. Bertrand M. Roehner, 2004. "Stock markets are not what we think they are: the key roles of cross-ownership and corporate treasury stock," Papers cond-mat/0406704, arXiv.org.
    4. Florin Turcaș & Florin Cornel Dumiter & Marius Boiță, 2022. "Econophysics Techniques and Their Applications on the Stock Market," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    6. Herrmann-Pillath, Carsten, 2008. "Neuroeconomics, naturalism and language," Frankfurt School - Working Paper Series 108, Frankfurt School of Finance and Management.
    7. Yan, C. & Zhang, J.W. & Zhang, Y. & Tang, Y.N., 2005. "Power–law properties of Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 425-432.
    8. Maslov, Sergei & Roehner, Bertrand M, 2004. "The conundrum of stock versus bond prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 164-182.
    9. Kozłowska, M. & Denys, M. & Wiliński, M. & Link, G. & Gubiec, T. & Werner, T.R. & Kutner, R. & Struzik, Z.R., 2016. "Dynamic bifurcations on financial markets," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 126-142.
    10. Haven, Emmanuel & Sozzo, Sandro, 2016. "A generalized probability framework to model economic agents' decisions under uncertainty," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 297-303.
    11. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    12. Schinckus, Christophe, 2018. "Ising model, econophysics and analogies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 95-103.
    13. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    14. R. Kitt & J. Kalda, 2006. "Leptokurtic portfolio theory," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 141-145, March.
    15. T. Kaizoji, 2006. "A precursor of market crashes: Empirical laws of Japan's internet bubble," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 123-127, March.
    16. Peter Richmond & Bertrand M. Roehner, 2017. "Property bubble in Hong Kong: A predicted decade-long slump (2016–2025)," Evolutionary and Institutional Economics Review, Springer, vol. 14(1), pages 79-99, June.
    17. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
    18. Maciej Jagielski & Ryszard Kutner, 2013. "Modelling the income distribution in the European Union: An application for the initial analysis of the recent worldwide financial crisis," Papers 1312.2362, arXiv.org.
    19. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    20. Bertrand M. Roehner, 2010. "Fifteen years of econophysics: worries, hopes and prospects," Papers 1004.3229, arXiv.org.

    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:wsi:ijmpcx:v:19:y:2008:i:03:n:s012918310801225x. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.