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Power variation & stochastic volatility: a review and some new results

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Author Info
Ole E. Barndorff-Nielsen () (The Centre for Mathematical Physics and Stochastics (MaPhySto), University of Aarhus, Denmark)
Svend Erik Graversen () (Department of Mathematical Sciences, University of Aarhus, Denmark)
Neil Shephard () (Nuffield College, University of Oxford, UK)

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Abstract

In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in financial econometrics in the analysis of volatility. The paper also provides some new results and discusses open issues.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W19/heyde2.pdf
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Publisher Info
Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2003-W19.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length: 13 pages
Date of creation: 15 Sep 2003
Date of revision:
Handle: RePEc:nuf:econwp:0319

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

For technical questions regarding this item, or to correct its listing, contact: (Catherine McNeill).

Related research
Keywords: Bipower Mixed Gaussian limit Power variation Quadratic variation Realised variance Realised volatility Stochastic volatility.

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References listed on IDEAS
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  1. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Jeannette H.C. Woerner, 2002. "Variational Sums and Power Variation: a unifying approach to model selection and estimation in semimartingale models," OFRC Working Papers Series 2002mf05, Oxford Financial Research Centre. [Downloadable!]
  7. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-. [Downloadable!]
    Other versions:
  9. 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. [Downloadable!] (restricted)
    Other versions:
  10. Jeannette H.C. Woerner, 2003. "Estimation of Integrated Volatility in Stochastic Volatility Models," OFRC Working Papers Series 2003mf05, Oxford Financial Research Centre. [Downloadable!]
  11. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  12. 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. [Downloadable!] (restricted)
    Other versions:
  13. 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. [Downloadable!] (restricted)
  14. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO. [Downloadable!]
    Other versions:
  15. 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.
  16. 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. [Downloadable!] (restricted)
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