IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v137y2018icp142-147.html
   My bibliography  Save this article

New and refined bounds for expected maxima of fractional Brownian motion

Author

Listed:
  • Borovkov, Konstantin
  • Mishura, Yuliya
  • Novikov, Alexander
  • Zhitlukhin, Mikhail

Abstract

For the fractional Brownian motion BH with the Hurst parameter value H in (0,1∕2), we derive new upper and lower bounds for the difference between the expectations of the maximum of BH over [0,1] and the maximum of BH over the discrete set of values in−1, i=1,…,n. We use these results to improve our earlier upper bounds for the expectation of the maximum of BH over [0,1] and derive new upper bounds for Pickands’ constant.

Suggested Citation

  • Borovkov, Konstantin & Mishura, Yuliya & Novikov, Alexander & Zhitlukhin, Mikhail, 2018. "New and refined bounds for expected maxima of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 142-147.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:142-147
    DOI: 10.1016/j.spl.2018.01.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715218300361
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.01.025?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. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    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. Krzysztof Bisewski & Krzysztof Dȩbicki & Tomasz Rolski, 2022. "Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ H = 1," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 53-68, October.

    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. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    2. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    3. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    4. Stefano De Marco, 2020. "On the harmonic mean representation of the implied volatility," Papers 2007.03585, arXiv.org.
    5. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    6. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    7. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    8. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    9. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.
    10. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2019. "Is Volatility Rough ?," Papers 1905.04852, arXiv.org, revised May 2019.
    11. Siu Hin Tang & Mathieu Rosenbaum & Chao Zhou, 2023. "Forecasting Volatility with Machine Learning and Rough Volatility: Example from the Crypto-Winter," Papers 2311.04727, arXiv.org, revised Feb 2024.
    12. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    13. Hans Buhler & Blanka Horvath & Terry Lyons & Imanol Perez Arribas & Ben Wood, 2020. "A Data-driven Market Simulator for Small Data Environments," Papers 2006.14498, arXiv.org.
    14. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2018. "The Alpha-Heston Stochastic Volatility Model," Papers 1812.01914, arXiv.org.
    15. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.
    16. Mathieu Rosenbaum & Jianfei Zhang, 2022. "On the universality of the volatility formation process: when machine learning and rough volatility agree," Papers 2206.14114, arXiv.org.
    17. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    18. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    19. Alexandre Pannier & Cristopher Salvi, 2024. "A path-dependent PDE solver based on signature kernels," Papers 2403.11738, arXiv.org.
    20. Martin Keller-Ressel & Martin Larsson & Sergio Pulido, 2018. "Affine Rough Models," Papers 1812.08486, 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:eee:stapro:v:137:y:2018:i:c:p:142-147. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.