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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

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Author Info

  • 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 inte- grated, 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, in- volving 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 pre- mium, 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.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-05.

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Length: 49
Date of creation: 17 Feb 2009
Date of revision:
Handle: RePEc:aah:create:2009-05

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Equilibrium asset pricing; stochastic volatility; leverage effect; volatility feed-back; option implied volatility; realized volatility; variance risk premium;

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References

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  1. John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
  2. Tim Bollerslev & Michael Gibson & Hao Zhou, 2007. "Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities," CREATES Research Papers 2007-16, School of Economics and Management, University of Aarhus.
  3. repec:oxf:wpaper:264 is not listed on IDEAS
  4. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics, EconWPA 0305004, EconWPA.
  5. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
  6. 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.
  7. 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, Elsevier, vol. 1(1), pages 83-106, June.
  8. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
  9. 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, 04.
  10. 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.
  11. 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.
  12. John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc.
  13. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  14. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  15. 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.
  16. 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, 08.
  17. Epstein, Larry G & Zin, Stanley E, 1989. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework," Econometrica, Econometric Society, Econometric Society, vol. 57(4), pages 937-69, July.
  18. 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.
  19. Tim Bollerslev & Tzuo Hao & George Tauchen, 2008. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2008-48, School of Economics and Management, University of Aarhus.
  20. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
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Citations

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Cited by:
  1. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2010. "Asymmetry and Long Memory in Volatility Modelling," Working Papers in Economics 10/60, University of Canterbury, Department of Economics and Finance.
  2. 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.
  3. Tim Bollerslev & James Marrone & Lai Xu & Hao Zhou, 2011. "Stock return predictability and variance risk premia: statistical inference and international evidence," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2011-52, Board of Governors of the Federal Reserve System (U.S.).
  4. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  5. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  6. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Tinbergen Institute Discussion Papers 14-037/III, Tinbergen Institute.
  7. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.
  8. Mario Jovanovic, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen 0240, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  9. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Working Papers in Economics 14/10, University of Canterbury, Department of Economics and Finance.
  10. 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.
  11. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.

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