IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v08y2005i02ns0219024905002937.html
   My bibliography  Save this article

Pathwise Identification Of The Memory Function Of Multifractional Brownian Motion With Application To Finance

Author

Listed:
  • SERGIO BIANCHI

    (University of Cassino, Faculty of Economics, Via S. Angelo, 03043 Cassino, Italy)

Abstract

We extend and adapt a class of estimators of the parameter H of the fractional Brownian motion in order to estimate the (time-dependent) memory function of a multifractional process. We provide: (a) the estimator's distribution when H ∈ (0,3/4); (b) the confidence interval under the null hypothesis H = 1/2; (c) a scaling law, independent on the value of H, discriminating between fractional and multifractional processes. Furthermore, assuming as a model for the price process the multifractional Brownian motion, empirical evidence is offered which is able to conciliate the inconsistent results achieved in estimating the intensity of dependence in financial time series.

Suggested Citation

  • Sergio Bianchi, 2005. "Pathwise Identification Of The Memory Function Of Multifractional Brownian Motion With Application To Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 255-281.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:n:s0219024905002937
    DOI: 10.1142/S0219024905002937
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024905002937
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024905002937?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. Axel A. Araneda, 2023. "A multifractional option pricing formula," Papers 2303.16314, arXiv.org.
    2. Sergio Bianchi & Massimiliano Frezza, 2018. "Liquidity, Efficiency and the 2007-2008 Global Financial Crisis," Annals of Economics and Finance, Society for AEF, vol. 19(2), pages 375-404, November.
    3. Matthieu Garcin, 2019. "Hurst Exponents And Delampertized Fractional Brownian Motions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-26, August.
    4. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    5. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    6. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Papers math/0703832, arXiv.org.
    7. Cadoni, Marinella & Melis, Roberta & Trudda, Alessandro, 2017. "Pension funds rules: Paradoxes in risk control," Finance Research Letters, Elsevier, vol. 22(C), pages 20-29.
    8. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    9. Sergio, Bianchi & Alessandro, Trudda, 2008. "Global Asset Return in Pension Funds: a dynamical risk analysis," MPRA Paper 12011, University Library of Munich, Germany, revised 14 Jun 2008.
    10. Marinella Cadoni & Roberta Melis & Alessandro Trudda, 2015. "Financial Crisis: A New Measure for Risk of Pension Fund Portfolios," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-12, June.
    11. Frezza, Massimiliano, 2012. "Modeling the time-changing dependence in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1510-1520.
    12. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    13. Frezza, Massimiliano, 2014. "Goodness of fit assessment for a fractal model of stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 41-50.
    14. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2006. "A Limit Theorem for Financial Markets with Inert Investors," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 789-810, November.
    15. Frezza, Massimiliano & Bianchi, Sergio & Pianese, Augusto, 2021. "Fractal analysis of market (in)efficiency during the COVID-19," Finance Research Letters, Elsevier, vol. 38(C).
    16. Bianchi, Sergio & Pianese, Augusto, 2018. "Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 64-75.
    17. Massimiliano Frezza & Sergio Bianchi & Augusto Pianese, 2022. "Forecasting Value-at-Risk in turbulent stock markets via the local regularity of the price process," Computational Management Science, Springer, vol. 19(1), pages 99-132, January.
    18. M. Cadoni & R. Melis & A. Trudda, 2012. "Financial crisis: a new measure for risk of pension funds assets," Working Paper CRENoS 201231, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

    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:ijtafx:v:08:y:2005:i:02:n:s0219024905002937. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.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.