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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

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  • Tim Bollerslev
  • Natalia Sizova
  • George Tauchen

Abstract

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the volatility, features short memory. This paper develops the first internally consistent equilibrium-based explanation for all these empirical facts. Using newly available high-frequency intraday data for the S&P 500 and the VIX volatility index, the authors show that the qualitative implications from the new theoretical continuous-time model match remarkably well with the distinct shapes and patterns in the sample autocorrelations and dynamic cross-correlations actually observed in the data. Copyright 2011, Oxford University Press.

Suggested Citation

  • Tim Bollerslev & Natalia Sizova & George Tauchen, 2011. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," Review of Finance, European Finance Association, vol. 16(1), pages 31-80.
    • Handle: RePEc:oup:revfin:v:16:y:2011:i:1:p:31-80
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    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.
    2. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
    3. 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.
    4. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    5. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    9. Luca Benzoni & Pierre Collin-Dufresne & Robert S. Goldstein, 2005. "Can Standard Preferences Explain the Prices of out of the Money S&P 500 Put Options," NBER Working Papers 11861, National Bureau of Economic Research, Inc.
    10. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    11. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    12. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    13. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
    14. 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.
    15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    16. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    17. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
    18. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    19. repec:oxf:wpaper:264 is not listed on IDEAS
    20. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    21. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
    22. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    23. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
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    Cited by:

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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. repec:zbw:rwirep:0240 is not listed on IDEAS
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Geert Bekaert & Eric Engstrom, 2009. "Asset Return Dynamics under Bad Environment Good Environment Fundamentals," NBER Working Papers 15222, National Bureau of Economic Research, Inc.
    14. 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.
    15. 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.
    16. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    17. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, New Economic School (NES).
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.

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    More about this item

    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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