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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

  • Tim Bollerslev
  • Natalia Sizova
  • George Tauchen

Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the volatility, is distinctly less persistent and appears short-memory. This paper develops the first internally consistent equilibrium based explanation for all of these empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. Our empirical investigations are made possible through the use of newly available high-frequency intra-day data for the VIX volatility index, along with corresponding high-frequency data for the S&P 500 aggregate market portfolio. We show that the qualitative implications from the new theoretical model match remarkably well with the distinct shapes and patterns in the sample auto-correlations and dynamic cross-correlations in the returns and volatilities observed in the data.

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Paper provided by Duke University, Department of Economics in its series Working Papers with number 10-34.

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Length: 52
Date of creation: 2010
Date of revision:
Handle: RePEc:duk:dukeec:10-34
Contact details of provider: Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
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Web page: http://econ.duke.edu/

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  1. 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.
  2. Geert Bekaert & Eric Engstrom & Yuhang Xing, 2006. "Risk, Uncertainty and Asset Prices," NBER Working Papers 12248, National Bureau of Economic Research, Inc.
  3. 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.
  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  5. repec:oxf:wpaper:264 is not listed on IDEAS
  6. 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.
  7. Tim Bollerslev & Hao Zhou, 2007. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2007-17, School of Economics and Management, University of Aarhus.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
  13. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
  14. Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
  15. Ravi Bansal & Amir Yaron, 2000. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," NBER Working Papers 8059, National Bureau of Economic Research, Inc.
  16. Tim Bollerslev & Michael Gibson & Hao Zhou, 2004. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Finance and Economics Discussion Series 2004-56, Board of Governors of the Federal Reserve System (U.S.).
  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. 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.
  19. 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.
  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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