IDEAS home Printed from
   My bibliography  Save this paper

Subdynamics of financial data from fractional Fokker-Planck equation


  • Janczura, Joanna
  • Wyłomańska, Agnieszka


In exhibition of many real market data we observe characteristic traps. This behavior is especially noticeable for processes corresponding to stock prices. Till now, such economic systems were analyzed in the following manner: before the further investigation trap-data were removed or omitted and then the conventional methods used. Unfortunately, for many observations this approach seems not to be reasonable therefore we propose an alternative approach based on the subdiffusion models that demonstrate such characteristic behavior and their corresponding probability density function (pdf) is described by the fractional Fokker-Planck equation. In this paper we model market data using subdiffusion with a constant force. We demonstrate properties of the considered systems and propose estimation methods.

Suggested Citation

  • Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:30649

    Download full text from publisher

    File URL:
    File Function: original version
    Download Restriction: no

    References listed on IDEAS

    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Sebastian, Orzeł & Agnieszka, Wyłomańska, 2010. "Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times," MPRA Paper 28593, University Library of Munich, Germany.
    2. Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
    3. repec:eee:apmaco:v:332:y:2018:i:c:p:197-208 is not listed on IDEAS
    4. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665,, revised Aug 2017.
    5. Gu, Hui & Liang, Jin-Rong & Zhang, Yun-Xiu, 2012. "Time-changed geometric fractional Brownian motion and option pricing with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3971-3977.
    6. repec:eee:phsmap:v:486:y:2017:i:c:p:628-637 is not listed on IDEAS

    More about this item


    subdiffusion; constant periods; fractional Fokker-Planck equation; stock prices;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation


    Access and download statistics


    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:pra:mprapa:30649. 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: (Joachim Winter). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.