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Realised power variation and stochastic volatility models

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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

Limit distribution results on realised power variation, that is sums of absolute powers of increments of a process, are derived for certain types of semimartingale with continuous local martingale component, in particular for a class of flexible stochastic volatility models. The theory cover, for example, the cases of realised volatility and realised absolute variation. Such results should be helpful in, for example, the analysis of volatility models using high frequency information.

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File URL: http://www.nuff.ox.ac.uk/Economics/papers/2001/w18/rth_order.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-W18.

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Length: 23 pages
Date of creation: 03 Oct 2001
Date of revision:
Handle: RePEc:nuf:econwp:0118

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

Related research

Keywords: Absolute returns; Mixed asymptotic normality; Realised volatility; p-variation; Quadratic variation; Semimartingale.;

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References

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  12. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO.
  13. 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.
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  20. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  21. 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.
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