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Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

  • Tim Bollerslev

    ()

    (Department of Economics, Duke University and CREATES)

  • Natalia Sizova

    ()

    (Department of Economics, Duke University)

  • George Tauchen

    ()

    (Department of Economics, Duke University)

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.

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File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_05.pdf
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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
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. 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.
  2. 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.
  3. 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.).
  4. John Y. Campbell, 1995. "Understanding Risk and Return," Harvard Institute of Economic Research Working Papers 1711, Harvard - Institute of Economic Research.
  5. 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.
  6. 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.
  7. Tim Bollerslev & Hao Zhou, 2006. "Expected stock returns and variance risk premia," Finance and Economics Discussion Series 2007-11, Board of Governors of the Federal Reserve System (U.S.).
  8. 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.
  9. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO.
  10. 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.
  11. 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.
  12. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA.
  13. 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.
  14. Itamar Drechsler & Amir Yaron, 2008. "What's Vol Got to Do With It," 2008 Meeting Papers 282, Society for Economic Dynamics.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. repec:oxf:wpaper:264 is not listed on IDEAS
  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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