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Volatility conditional on price trends

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  • Gilles Zumbach

Abstract

The influence of the past price behaviour on the realized volatility is investigated, showing that trending (driftless) prices lead to increased (decreased) realized volatility. This 'volatility induced by trend' constitutes a new stylized fact. The past price behaviour is measured by the product of two non-overlapping returns (of the form r × L[r] where L is the lag operator), and is different from the usual heteroskedasticity. The effect is studied empirically using USD/CHF foreign exchange data, in a large range of time horizons. On the modelling side, a set of ARCH based processes are modified in order to include the 'volatility induced by trend' effect, and their forecasting performances are compared. The aim is to understand the role and importance of the various terms that can be included in such a model. For a better forecast, it is shown that the main factor is the shape of the memory kernel (i.e. power law), and the next most important factor is the trend effect. The subtle role of mean reversion is also discussed.

Suggested Citation

  • Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:4:p:431-442
    DOI: 10.1080/14697680903266730
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    References listed on IDEAS

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    Cited by:

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    2. Léo Parent, 2022. "The EWMA Heston model," Post-Print hal-04431111, HAL.
    3. Marcel Nutz & Andr'es Riveros Valdevenito, 2023. "On the Guyon-Lekeufack Volatility Model," Papers 2307.01319, arXiv.org, revised Jul 2024.
    4. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    5. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Quantitative Finance, Taylor & Francis Journals, vol. 23(9), pages 1221-1258, September.
    6. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "The fine-structure of volatility feedback I: multi-scale self-reflexivity," Papers 1206.2153, arXiv.org, revised Sep 2013.
    7. 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.
    8. 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.
    9. R'emy Chicheportiche, 2013. "Non-linear dependences in finance," Papers 1309.5073, arXiv.org.
    10. Jinniao Qiu & Antony Ware & Yang Yang, 2024. "Stochastic Path-Dependent Volatility Models for Price-Storage Dynamics in Natural Gas Markets and Discrete-Time Swing Option Pricing," Papers 2406.16400, arXiv.org.
    11. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    12. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    13. Guido Gazzani & Julien Guyon, 2024. "Pricing and calibration in the 4-factor path-dependent volatility model," Papers 2406.02319, arXiv.org.
    14. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.
    15. Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    16. Aditi Dandapani & Paul Jusselin & Mathieu Rosenbaum, 2019. "From quadratic Hawkes processes to super-Heston rough volatility models with Zumbach effect," Papers 1907.06151, arXiv.org, revised Jan 2021.

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