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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
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    References listed on IDEAS

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    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. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    4. 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.
    5. 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.
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