IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v4y2002i1d10.1023_a1015753313674.html
   My bibliography  Save this article

Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set

Author

Listed:
  • Rimas Norvaiša

    (Institute of Mathematics and Informatics)

  • Donna Mary Salopek

    (York University)

Abstract

In this paper we apply a real analysis approach to test continuous time stochastic models of financial mathematics. Specifically, fractal dimension estimation methods are applied to statistical analysis of continuous time stochastic processes. To estimate a roughness of a sample function we modify a box-counting method typically used in estimating fractal dimension of a graph of a function. Here the roughness of a function f is defined as the infimum of numbers p > 0 such that f has bounded p-variation, which we call the p-variation index of f. The method is also tested on estimating the exponent α∈[1, 2] of a simulated symmetric α-stable process, and on estimating the Hurst exponent H ∈ (0, 1) of a simulated fractional Brownian motion.

Suggested Citation

  • Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:1:d:10.1023_a:1015753313674
    DOI: 10.1023/A:1015753313674
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1015753313674
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1015753313674?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. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
    2. Mark E. Crovella & Murad S. Taqqu, 1999. "Estimating the Heavy Tail Index from Scaling Properties," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 55-79, July.
    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. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    2. Jamison Wolf, 2010. "Random Fractals Determined by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1182-1203, December.
    3. Xiaochuan Yang, 2018. "Hausdorff Dimension of the Range and the Graph of Stable-Like Processes," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2412-2431, December.

    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. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    2. Alexander Schied & Leo Speiser & Iryna Voloshchenko, 2016. "Model-free portfolio theory and its functional master formula," Papers 1606.03325, arXiv.org, revised May 2018.
    3. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    4. John Armstrong & Claudio Bellani & Damiano Brigo & Thomas Cass, 2021. "Option pricing models without probability: a rough paths approach," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1494-1521, October.
    5. Henry Chiu & Rama Cont, 2023. "A model‐free approach to continuous‐time finance," Mathematical Finance, Wiley Blackwell, vol. 33(2), pages 257-273, April.
    6. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jan 2014.
    7. Alexander Alvarez & Sebastian E. Ferrando, 2016. "Trajectory-Based Models, Arbitrage And Continuity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-34, May.
    8. Henry Chiu & Rama Cont, 2022. "A model-free approach to continuous-time finance," Papers 2211.15531, arXiv.org.
    9. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2016. "A superhedging approach to stochastic integration," Papers 1609.02349, arXiv.org, revised Sep 2017.
    10. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    11. Alexander Alvarez & Sebastian Ferrando & Pablo Olivares, 2011. "Arbitrage and Hedging in a non probabilistic framework," Papers 1103.1006, arXiv.org.
    12. Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    13. Alexander Schied & Iryna Voloshchenko, 2015. "Pathwise no-arbitrage in a class of Delta hedging strategies," Papers 1511.00026, arXiv.org, revised Jun 2016.
    14. Mark Britten-Jones & Anthony Neuberger, 1996. "Arbitrage pricing with incomplete markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 347-363.
    15. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.
    16. Candia Riga, 2016. "A pathwise approach to continuous-time trading," Papers 1602.04946, arXiv.org.
    17. Schied, Alexander, 2014. "Model-free CPPI," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 84-94.
    18. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    19. Paulo M.M. Rodrigues & João Nicolau, 2015. "A New Regression-Based Tail Index Estimator: An Application to Exchange Rates," Working Papers w201514, Banco de Portugal, Economics and Research Department.
    20. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.

    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:metcap:v:4:y:2002:i:1:d:10.1023_a:1015753313674. 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: 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.