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Decoupling the Short- and Long-Term Behavior of Stochastic Volatility
[Multifactor Approximation of Rough Volatility Models]

Author

Listed:
  • Mikkel Bennedsen
  • Asger Lunde
  • Mikko S Pakkanen

Abstract

We introduce a new class of continuous-time models of the stochastic volatility of asset prices. The models can simultaneously incorporate roughness and slowly decaying autocorrelations, including proper long memory, which are two stylized facts often found in volatility data. Our prime model is based on the so-called Brownian semistationary process and we derive a number of theoretical properties of this process, relevant to volatility modeling. Applying the models to realized volatility measures covering a vast panel of assets, we find evidence consistent with the hypothesis that time series of realized measures of volatility are both rough and very persistent. Lastly, we illustrate the utility of the models in an extensive forecasting study; we find that the models proposed in this article outperform a wide array of benchmarks considerably, indicating that it pays off to exploit both roughness and persistence in volatility forecasting.

Suggested Citation

  • Mikkel Bennedsen & Asger Lunde & Mikko S Pakkanen, 2022. "Decoupling the Short- and Long-Term Behavior of Stochastic Volatility [Multifactor Approximation of Rough Volatility Models]," Journal of Financial Econometrics, Oxford University Press, vol. 20(5), pages 961-1006.
    • Handle: RePEc:oup:jfinec:v:20:y:2022:i:5:p:961-1006.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbaa049
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    Citations

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    Cited by:

    1. 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.
    2. Bolko, Anine E. & Christensen, Kim & Pakkanen, Mikko S. & Veliyev, Bezirgen, 2023. "A GMM approach to estimate the roughness of stochastic volatility," Journal of Econometrics, Elsevier, vol. 235(2), pages 745-778.
    3. Antoine Jacquier & Zan Zuric, 2023. "Random neural networks for rough volatility," Papers 2305.01035, arXiv.org.
    4. 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.
    5. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Minimax Theory," Papers 2210.01214, arXiv.org, revised Feb 2024.
    7. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Central limit theorems," Papers 2210.01216, arXiv.org, revised Jul 2023.
    8. Saad Mouti, 2023. "Rough volatility: evidence from range volatility estimators," Papers 2312.01426, arXiv.org.

    More about this item

    Keywords

    : Brownian semistationary process; forecasting; high-frequency data; long memory; persistence; rough volatility; stochastic volatility;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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