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Estimating quadratic variation using realised volatility

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Author Info

  • Ole E. Barndorff-Nielsen

    ()
    (The Centre for Mathematical Physics and Stochastics (MaPhySto), University of Aarhus)

  • Neil Shephard

    ()
    (Nuffield College, Oxford)

Abstract

This paper looks at some recent work on estimating quadratic variation using realised volatility (RV) - that is sums of M squared returns. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent estimator of quadratic variation (QV). We express concern that without additonal assumptions it seems difficult to given any measure of uncertainty of the RV in this context. The position dramatically changes when we work with a rather general SV model - which is a special case of the semimartingale model. Then QV is integrated volatility and we can derive the asymptotic distribution of the RV and its rate of convergence. These results do not require us to specify a model for either the drift or volatility functions, although we have to impose some weak regularity assumptions. We illustrate the use of the limit theory on some exchange rate data. We show that even with the large values of M and RV is sometimes a quite noisy estimator of integrated volatility

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File URL: http://www.nuff.ox.ac.uk/Economics/papers/2001/w20/jae.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2001-W20.

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Length: 18 pages
Date of creation: 01 Sep 2001
Date of revision: 01 Nov 2001
Handle: RePEc:nuf:econwp:0120

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: Power variation; Quadratic variation; Realised volatility; Semimartingale; Volatility.;

This paper has been announced in the following NEP Reports:

References

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  1. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
  2. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 1-1, January.
  3. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9613, Universite de Montreal, Departement de sciences economiques.
  4. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Econometric Analysis of Realised Covariation: High Frequency Covariance, Regression and Correlation in Financial Economics," Economics Papers, Economics Group, Nuffield College, University of Oxford 2002-W13, Economics Group, Nuffield College, University of Oxford, revised 18 Mar 2002.
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  6. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 353, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 63(2), pages 167-241.
  8. G. William Schwert, 1997. "Stock Market Volatility: Ten Years After the Crash," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 97-51, Wharton School Center for Financial Institutions, University of Pennsylvania.
  9. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2001-26, Universite de Montreal, Departement de sciences economiques.
  10. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, Elsevier, vol. 8(4), pages 323-361, December.
  11. Andreou, Elena & Ghysels, Eric, 2002. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation, and Empirical Results," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 363-76, July.
  12. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers, Economics Group, Nuffield College, University of Oxford 2001-W16, Economics Group, Nuffield College, University of Oxford.
  14. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  16. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  17. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers, University of Oxford, Department of Economics 2005-W17, University of Oxford, Department of Economics.
  18. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  19. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(4), pages 317-340, December.
  20. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 50(2), pages 125-150, November.
  21. Matthew Richardson & James H. Stock, 1990. "Drawing Inferences From Statistics Based on Multi-Year Asset Returns," NBER Working Papers 3335, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Peter Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models:The Model Confidence Set Approach," Working Papers, Brown University, Department of Economics 2003-05, Brown University, Department of Economics.
  2. Nour Meddahi, 2001. "A Theoretical Comparison Between Integrated andRealized Volatilities / A Theoretical Comparison Between Integrated and Realized Volatilities," CIRANO Working Papers, CIRANO 2001s-71, CIRANO.

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