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Realized Volatility and Multipower Variation

  • Torben G. Andersen

    ()

    (Kellogg School of Management, Northwestern University and CREATES)

  • Viktor Todorov

    ()

    (Kellogg School of Management, Northwestern University)

This paper reviews basic notions of return variation in the context of a continuous-time arbitrage-free asset pricing model and discusses some of their applications. We first define return variation in the infeasible continuous-sampling case. Then we introduce realized measures obtained from high-frequency observations which provide consistent and asymptotically normal estimates of the underlying return variation. The paper discusses applications of these measures for reduced-form volatility modeling and forecasting as well as testing for the presence of jumps.

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File URL: ftp://ftp.econ.au.dk/creates/rp/09/rp09_49.pdf
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-49.

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Length: 14
Date of creation: 01 May 2009
Date of revision:
Handle: RePEc:aah:create:2009-49
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Torben G. Andersen & Tim Bollerslev & Dobrislav Dobrev, 2007. "No-Arbitrage Semi-Martingale Restrictions for Continuous-Time Volatility Models subject to Leverage Effects, Jumps and i.i.d. Noise: Theory and Testable Distributional Implications," NBER Working Papers 12963, National Bureau of Economic Research, Inc.
  2. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  3. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  4. Neil Shephard & Matthias Winkel & Ole E. Barndorff-Nielsen, 2005. "Limit theorems for multipower variation in the presence of jumps," Economics Series Working Papers 2005-FE-06, University of Oxford, Department of Economics.
  5. repec:oxf:wpaper:264 is not listed on IDEAS
  6. 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.).
  7. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  8. 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.
  9. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  10. Federico Bandi & Jeffrey Russell & Yinghua Zhu, 2008. "Using High-Frequency Data in Dynamic Portfolio Choice," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 163-198.
  11. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  12. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns," Working Papers 1173, Queen's University, Department of Economics.
  13. Officer, R R, 1973. "The Variability of the Market Factor of the New York Stock Exchange," The Journal of Business, University of Chicago Press, vol. 46(3), pages 434-53, July.
  14. 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.
  15. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
  16. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  17. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
  18. Almut Elisabeth Dorothea Veraart, 2007. "Feasible inference for realised variance in the presence of jumps," Economics Series Working Papers 2007-FE-02, University of Oxford, Department of Economics.
  19. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  20. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Series Working Papers 2003-W12, University of Oxford, Department of Economics.
  21. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  22. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," NBER Working Papers 10914, National Bureau of Economic Research, Inc.
  23. Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Series Working Papers 2004-FE-21, University of Oxford, Department of Economics.
  24. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
  25. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  26. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  27. Mark Podolskij & Mathias Vetter, 2007. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," CREATES Research Papers 2007-27, School of Economics and Management, University of Aarhus.
  28. Jiang, George J. & Oomen, Roel C.A., 2008. "Testing for jumps when asset prices are observed with noise-a "swap variance" approach," Journal of Econometrics, Elsevier, vol. 144(2), pages 352-370, June.
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