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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. 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.
  2. 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.
  3. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2006. "Risk, Uncertainty and Asset Prices," CEPR Discussion Papers 5947, C.E.P.R. Discussion Papers.
  4. 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.
  5. John Y. Campbell, 1993. "Understanding Risk and Return," NBER Working Papers 4554, National Bureau of Economic Research, Inc.
  6. 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.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc.
  8. 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.
  9. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO.
  10. 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.
  11. repec:oxf:wpaper:264 is not listed on IDEAS
  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. 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.
  16. 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.
  17. 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.
  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. 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, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," KIER Working Papers 848, Kyoto University, Institute of Economic Research.
  2. 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.
  3. Yacine Ait-Sahalia & Jianqing Fan & Yingying Li, 2011. "The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency," NBER Working Papers 17592, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. 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.
  7. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Documentos del Instituto Complutense de Análisis Económico 2014-05, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  8. Manabu Asai & Michael McAleer, 2013. "A Fractionally Integrated Wishart Stochastic Volatility Model," Tinbergen Institute Discussion Papers 13-025/III, Tinbergen Institute.
  9. 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.).
  10. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
  11. 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.

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