IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v17y2024i4p131-d1361912.html
   My bibliography  Save this article

A New Proxy for Estimating the Roughness of Volatility

Author

Listed:
  • Qi Zhao

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
    These authors contributed equally to this work.)

  • Alexandra Chronopoulou

    (Department of Statistics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a new proxy for the unobserved volatility process that will allow us to better understand and hence model a rough or persistent volatility. Starting with a stochastic volatility model with minimal assumptions on the volatility process, we calibrate the model to options’ data and their sensitivities to obtain an implied volatility process. Starting with this new proxy, we then study the roughness/persistence of the volatility using S&P 500 European put option daily data. We then estimate the Hurst index, i.e., roughness/smoothness parameter, of the volatility with various techniques to find that the volatility does exhibit a rough behavior, even in a low-frequency framework.

Suggested Citation

  • Qi Zhao & Alexandra Chronopoulou, 2024. "A New Proxy for Estimating the Roughness of Volatility," JRFM, MDPI, vol. 17(4), pages 1-15, March.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:4:p:131-:d:1361912
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/17/4/131/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/17/4/131/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    2. José Da Fonseca & Wenjun Zhang, 2019. "Volatility of volatility is (also) rough," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 600-611, May.
    3. Mark. B. Garman., 1976. "A General Theory of Asset Valuation under Diffusion State Processes," Research Program in Finance Working Papers 50, University of California at Berkeley.
    4. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    5. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    7. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    8. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    Full references (including those not matched with items on IDEAS)

    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. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
    2. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François & Jayaraman, Sarath Kumar, 2025. "A general option pricing framework for affine fractionally integrated models," Journal of Banking & Finance, Elsevier, vol. 171(C).
    3. Yicun Li & Yuanyang Teng, 2022. "Estimation of the Hurst Parameter in Spot Volatility," Mathematics, MDPI, vol. 10(10), pages 1-26, May.
    4. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    5. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Papers 2105.09140, arXiv.org, revised Sep 2021.
    6. 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.
    7. Hiroyuki Kawakatsu, 2022. "Modeling Realized Variance with Realized Quarticity," Stats, MDPI, vol. 5(3), pages 1-25, September.
    8. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    9. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    10. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    11. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    12. Giulia Di Nunno & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2022. "Option pricing in Sandwiched Volterra Volatility model," Papers 2209.10688, arXiv.org, revised Jul 2024.
    13. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675, arXiv.org, revised Mar 2019.
    14. Rama Cont & Purba Das, 2022. "Rough volatility: fact or artefact?," Papers 2203.13820, arXiv.org, revised Jul 2023.
    15. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175.
    16. Matthieu Garcin & Martino Grasselli, 2022. "Long versus short time scales: the rough dilemma and beyond," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 257-278, June.
    17. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    18. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    19. Jia Li & Peter C. B. Phillips & Shuping Shi & Jun Yu, 2022. "Weak Identification of Long Memory with Implications for Inference," Economics and Statistics Working Papers 8-2022, Singapore Management University, School of Economics.
    20. Nourdin, Ivan & Diu Tran, T.T., 2019. "Statistical inference for Vasicek-type model driven by Hermite processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3774-3791.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:gam:jjrfmx:v:17:y:2024:i:4:p:131-:d:1361912. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.