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Realized volatility

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  • 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. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  11. 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.
  12. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO.
  13. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
  14. 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.
  15. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  16. 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.).
  17. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2005. "Explaining credit default swap spreads with the equity volatility and jump risks of individual firms," Finance and Economics Discussion Series 2005-63, Board of Governors of the Federal Reserve System (U.S.).
  18. 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.
  19. 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.
  20. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
  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. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
  2. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics," OFRC Working Papers Series 2002fe03, Oxford Financial Research Centre.
  3. 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.
  4. 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.
  5. Wang, Jianxin, 2013. "Liquidity commonality among Asian equity markets," Pacific-Basin Finance Journal, Elsevier, vol. 21(1), pages 1209-1231.
  6. Davies, Laurie & Höhenrieder, Christian & Krämer, Walter, 2012. "Recursive computation of piecewise constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3623-3631.
  7. 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.
  8. 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.).
  9. 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.
  10. 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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