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The Reactive Volatility Model

Author

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  • Sebastien Valeyre
  • Denis Grebenkov
  • Sofiane Aboura
  • Qian Liu

Abstract

We present a new volatility model, simple to implement, that includes a leverage effect whose return-volatility correlation function fits to empirical observations. This model is able to capture both the "retarded effect" induced by the specific risk, and the "panic effect", which occurs whenever systematic risk becomes the dominant factor. Consequently, in contrast to a GARCH model and a standard volatility estimate from the squared returns, this new model is as reactive as the implied volatility: the model adjusts itself in an instantaneous way to each variation of the single stock price or the stock index price and the adjustment is highly correlated to implied volatility changes. We also test the reactivity of our model using extreme events taken from the 470 most liquid European stocks over the last decade. We show that the reactive volatility model is more robust to extreme events, and it allows for the identification of precursors and replicas of extreme events.

Suggested Citation

  • Sebastien Valeyre & Denis Grebenkov & Sofiane Aboura & Qian Liu, 2012. "The Reactive Volatility Model," Papers 1209.5190, arXiv.org, revised Apr 2013.
    • Handle: RePEc:arx:papers:1209.5190
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    References listed on IDEAS

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    1. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    2. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    3. repec:dau:papers:123456789/10898 is not listed on IDEAS
    4. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    5. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    6. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    7. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    8. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
    9. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
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    Citations

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    Cited by:

    1. Sebastien Valeyre & Sofiane Aboura & Denis Grebenkov, 2019. "The Reactive Beta Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 42(1), pages 71-113, March.
    2. Sebastien Valeyre, 2020. "Refined model of the covariance/correlation matrix between securities," Papers 2001.08911, arXiv.org.
    3. Sebastien Valeyre, 2022. "Optimal trend following portfolios," Papers 2201.06635, arXiv.org.
    4. Sebastien Valeyre & Denis Grebenkov & Sofiane Aboura & Francois Bonnin, 2016. "Should employers pay their employees better? An asset pricing approach," Papers 1602.00931, arXiv.org, revised Oct 2016.

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    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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