IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Estimating quadratic variation using realized variance

  • Ole E. Barndorff-Nielsen

    (The Centre for Mathematical Physics and Stochastics (MaPhySto), University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark)

  • Neil Shephard

    (Nuffield College, University of Oxford, Oxford OX1 1NF, UK)

This paper looks at some recent work on estimating quadratic variation using realized variance (RV)-that is, sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high-frequency financial return data. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent (as M → ∞) estimator of quadratic variation (QV). We express concern that without additional assumptions it seems difficult to give 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 variance 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 and some stock data. We show that even with large values of M the RV is sometimes a quite noisy estimator of integrated variance. Copyright © 2002 John Wiley & Sons, Ltd.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://hdl.handle.net/10.1002/jae.691
File Function: Link to full text; subscription required
Download Restriction: no

File URL: http://qed.econ.queensu.ca:80/jae/2002-v17.5/
File Function: Supporting data files and programs
Download Restriction: no

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 5 ()
Pages: 457-477

as
in new window

Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:457-477
Contact details of provider: Web page: http://www.interscience.wiley.com/jpages/0883-7252/

Order Information: Web: http://www3.interscience.wiley.com/jcatalog/subscribe.jsp?issn=0883-7252 Email:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO.
  2. 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, vol. 63(2), pages 167-241.
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
  4. 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, vol. 39(4), pages 885-905, November.
  5. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  6. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  8. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  9. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Universite de Montreal, Departement de sciences economiques.
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  11. Poterba, James M & Summers, Lawrence H, 1986. "The Persistence of Volatility and Stock Market Fluctuations," American Economic Review, American Economic Association, vol. 76(5), pages 1142-51, December.
  12. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  13. G. William Schwert, 1997. "Stock Market Volatility: Ten Years After the Crash," Center for Financial Institutions Working Papers 97-51, Wharton School Center for Financial Institutions, University of Pennsylvania.
  14. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  15. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  16. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
  17. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
  18. Comte, F. & Renault, E., 1996. "Long Memory in Continuous Time Stochastic Volatility Models," Papers 96.406, Toulouse - GREMAQ.
  19. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  20. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:457-477. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.