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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

Author

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  • Tim Bollerslev

    (Department of Economics, Duke University and CREATES)

  • Natalia Sizova

    (Department of Economics, Duke University)

  • George Tauchen

    (Department of Economics, Duke University)

Abstract

Stock market volatility clusters in time, carries a risk premium, is fractionally integrated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. We show that the qualitative theoretical implications from the new model match remarkably well with the distinct shapes and patterns in the sample autocorrelations of the volatility and the volatility risk premium, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes.

Suggested Citation

  • Tim Bollerslev & Natalia Sizova & George Tauchen, 2009. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," CREATES Research Papers 2009-05, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2009-05
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    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
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    22. Bollerslev, Tim & Zhou, Hao, 2006. "Volatility puzzles: a simple framework for gauging return-volatility regressions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 123-150.
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    Cited by:

    1. Manabu Asai & Michael McAleer, 2017. "A fractionally integrated Wishart stochastic volatility model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 42-59, March.
    2. Yingying Xu & Donald Lien, 2022. "Forecasting volatilities of oil and gas assets: A comparison of GAS, GARCH, and EGARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 259-278, March.
    3. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 892-908, November.
    4. 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.
    5. Ilze Kalnina & Dacheng Xiu, 2017. "Nonparametric Estimation of the Leverage Effect: A Trade-Off Between Robustness and Efficiency," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 384-396, January.
    6. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    7. Bollerslev, Tim & Marrone, James & Xu, Lai & Zhou, Hao, 2014. "Stock Return Predictability and Variance Risk Premia: Statistical Inference and International Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(3), pages 633-661, June.
    8. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2012. "Asymmetry and Long Memory in Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 495-512, June.
    9. Jovanović, Mario, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers 240, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    10. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    11. Kanniainen, Juho & Piché, Robert, 2013. "Stock price dynamics and option valuations under volatility feedback effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 722-740.
    12. Christian Schlag & Michael Semenischev & Julian Thimme, 2021. "Predictability and the Cross-Section of Expected Returns: A Challenge for Asset Pricing Models," Management Science, INFORMS, vol. 67(12), pages 7932-7950, December.
    13. Eraker, Bjørn & Wang, Jiakou, 2015. "A non-linear dynamic model of the variance risk premium," Journal of Econometrics, Elsevier, vol. 187(2), pages 547-556.
    14. Jianjun Miao & Bin Wei & Hao Zhou, 2019. "Ambiguity Aversion and the Variance Premium," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 1-36, June.
    15. Geert Bekaert & Eric Engstrom, 2009. "Asset Return Dynamics under Bad Environment Good Environment Fundamentals," NBER Working Papers 15222, National Bureau of Economic Research, Inc.
    16. Andersen, Torben G. & Varneskov, Rasmus T., 2022. "Testing for parameter instability and structural change in persistent predictive regressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 361-386.
    17. Guglielmo Maria Caporale & Luis A. Gil-Alana & Miguel Martin-Valmayor, 2020. "Persistence in the Realized Betas: Some Evidence for the Spanish Stock Market," CESifo Working Paper Series 8171, CESifo.
    18. Senarathne Chamil W. & Šoja Tijana, 2019. "Heteroskedasticity in Excess Bitcoin Return Data: Google Trend vs. Garch Effects," Financial Sciences. Nauki o Finansach, Sciendo, vol. 24(3), pages 35-45, September.
    19. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, New Economic School (NES).
    20. Tim Bollerslev & Daniela Osterrieder & Natalia Sizova & George Tauchen, 2011. "Risk and Return: Long-Run Relationships, Fractional Cointegration, and Return Predictability," CREATES Research Papers 2011-51, Department of Economics and Business Economics, Aarhus University.
    21. repec:zbw:rwirep:0240 is not listed on IDEAS
    22. Mario Jovanovic, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers 0240, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    23. Schlag, Christian & Semenischev, Michael & Thimme, Julian, 2020. "Predictability and the cross-section of expected returns: A challenge for asset pricing models," SAFE Working Paper Series 289, Leibniz Institute for Financial Research SAFE.
    24. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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    More about this item

    Keywords

    Equilibrium asset pricing; stochastic volatility; leverage effect; volatility feed-back; option implied volatility; realized volatility; variance risk premium;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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