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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.

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Bibliographic Info

Article provided by European Finance Association in its journal Review of Finance.

Volume (Year): 16 (2011)
Issue (Month): 1 ()
Pages: 31-80

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Handle: RePEc:oup:revfin:v:16:y:2011:i:1:p:31-80

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References

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  1. 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.
  2. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
  3. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  4. 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.
  5. 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.
  6. repec:oxf:wpaper:264 is not listed on IDEAS
  7. Geert Bekaert & Eric Engstrom & Yuhang Xing, 2005. "Risk, uncertainty, and asset prices," Finance and Economics Discussion Series 2005-40, Board of Governors of the Federal Reserve System (U.S.).
  8. 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.
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers 2007-18, School of Economics and Management, University of Aarhus.
  10. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
  11. 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, vol. 57(4), pages 937-69, July.
  12. 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.
  13. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO.
  14. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
  15. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
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Cited by:
  1. 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.
  2. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," KIER Working Papers 848, Kyoto University, Institute of Economic Research.
  3. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  4. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2010. "Asymmetry and Long Memory in Volatility Modelling," KIER Working Papers 726, Kyoto University, Institute of Economic Research.
  5. 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.
  6. 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.
  7. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.
  8. 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.
  9. 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.
  10. 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 2011-52, Board of Governors of the Federal Reserve System (U.S.).

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