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Realized volatility

  • Torben G. Andersen
  • Luca Benzoni

Realized volatility is a nonparametric ex-post estimate of the return variation. The most obvious realized volatility measure is the sum of finely-sampled squared return realizations over a fixed time interval. In a frictionless market the estimate achieves consistency for the underlying quadratic return variation when returns are sampled at increasingly higher frequency. We begin with an account of how and why the procedure works in a simplified setting and then extend the discussion to a more general framework. Along the way we clarify how the realized volatility and quadratic return variation relate to the more commonly applied concept of conditional return variance. We then review a set of related and useful notions of return variation along with practical measurement issues (e.g., discretization error and microstructure noise) before briefly touching on the existing empirical applications.

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Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series with number WP-08-14.

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Date of creation: 2008
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Handle: RePEc:fip:fedhwp:wp-08-14
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  1. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model for Volatility Using Intra-Daily Data," NBER Working Papers 10117, National Bureau of Economic Research, Inc.
  2. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
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  6. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
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  10. Torben G. Andersen & Luca Benzoni, 2007. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification test for Affine Term Structure Models," NBER Working Papers 12962, National Bureau of Economic Research, Inc.
  11. 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.
  12. Jonathan Wright & Hao Zhou, 2007. "Bond risk premia and realized jump volatility," Finance and Economics Discussion Series 2007-22, Board of Governors of the Federal Reserve System (U.S.).
  13. Hui Guo & Christopher J. Neely & Jason Higbee, 2008. "Foreign Exchange Volatility Is Priced in Equities," Financial Management, Financial Management Association International, vol. 37(4), pages 769-790, December.
  14. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," CIRANO Working Papers 2004s-19, CIRANO.
  15. Bollerslev, Tim & Zhang, Benjamin Y. B., 2003. "Measuring and modeling systematic risk in factor pricing models using high-frequency data," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 533-558, December.
  16. Thomakos, Dimitrios D. & Wang, Tao, 2003. "Realized volatility in the futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 321-353, May.
  17. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
  18. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
  19. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  20. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  21. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
  22. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
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