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Realized volatility

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Author Info

  • Torben G. Andersen
  • Luca Benzoni

Abstract

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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Bibliographic Info

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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Keywords: Stochastic analysis;

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References

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  1. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model For Volatility Using Intra-Daily Data," Econometrics Working Papers Archive wp2003_07, Universita' degli Studi di Firenze, Dipartimento di Statistica "G. Parenti".
  2. Hui Guo & Christopher J. Neely & Jason Higbee, 2006. "Foreign exchange volatility is priced in equities," Working Papers 2004-029, Federal Reserve Bank of St. Louis.
  3. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
  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. 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.
  6. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
  7. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
  8. 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.
  9. 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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  11. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  12. Andrew Ang & Robert J. Hodrick & Yuhang Xing & Xiaoyan Zhang, 2006. "The Cross-Section of Volatility and Expected Returns," Journal of Finance, American Finance Association, vol. 61(1), pages 259-299, 02.
  13. Thomakos, Dimitrios D. & Wang, Tao, 2003. "Realized volatility in the futures markets," Journal of Empirical Finance, Elsevier, vol. 10(3), pages 321-353, May.
  14. Torben G. Andersen & Luca Benzoni, 2006. "Do bonds span volatility risk in the U.S. Treasury market? a specification test for affine term structure models," Working Paper Series WP-06-15, Federal Reserve Bank of Chicago.
  15. 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.
  16. 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.
  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. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.).
  19. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
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  21. 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.
  22. 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.
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Citations

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Cited by:
  1. Michel Beine & Oscar Bernal & Jean-Yves Gnabo & Christelle Lecourt, 2007. "Intervention Policy of the BoJ: a Unified Approach," LSF Research Working Paper Series 07-19, Luxembourg School of Finance, University of Luxembourg.
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics," Economics Papers 2002-W13, Economics Group, Nuffield College, University of Oxford, revised 18 Mar 2002.
  3. Michael W. Brandt & Francis X. Diebold, 2001. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," PIER Working Paper Archive 03-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Apr 2003.
  4. Alain P. Chaboud & Sergey Chernenko & Edward Howorka & Raj S. Krishnasami Iyer & David Liu & Jonathan H. Wright, 2004. "The high-frequency effects of U.S. macroeconomic data releases on prices and trading activity in the global interdealer foreign exchange market," International Finance Discussion Papers 823, Board of Governors of the Federal Reserve System (U.S.).
  5. Garland Durham, 2004. "Likelihood-based estimation and specification analysis of one- and two-factor SV models with leverage effects," Econometric Society 2004 North American Summer Meetings 294, Econometric Society.
  6. Lillie Lam & Laurence Fung & Ip-wing Yu, 2009. "Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes," Working Papers 0901, Hong Kong Monetary Authority.
  7. Wang, Jianxin & Yang, Minxian, 2011. "Housewives of Tokyo versus the gnomes of Zurich: Measuring price discovery in sequential markets," Journal of Financial Markets, Elsevier, vol. 14(1), pages 82-108, February.
  8. Guan Wang & Pierre Yourougou & Yue Wang, 2012. "Which implied volatility provides the best measure of future volatility?," Journal of Economics and Finance, Springer, vol. 36(1), pages 93-105, January.

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