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Realised power variation and stochastic volatility models

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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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  • Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Realised power variation and stochastic volatility models," Economics Papers 2001-W18, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0118
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    File URL: http://www.nuff.ox.ac.uk/Economics/papers/2001/w18/rth_order.pdf
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    22. 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.
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    Cited by:

    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Elena Andreou, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 290-318.
    3. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    4. Woerner Jeannette H. C., 2003. "Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 47-68, January.
    5. Sam Howison & Avraam Rafailidis & Henrik Rasmussen, 2004. "On the pricing and hedging of volatility derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 317-346.
    6. 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.
    7. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Multipower Variation and Stochastic Volatility," OFRC Working Papers Series 2004fe22, Oxford Financial Research Centre.
    8. Tauchen, George & Zhou, Hao, 2011. "Realized jumps on financial markets and predicting credit spreads," Journal of Econometrics, Elsevier, vol. 160(1), pages 102-118, January.
    9. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(04), pages 677-719, August.
    10. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    11. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    12. Ole E. Barndorff-Nielsen & Bent Nielsen & Neil Shephard & Carla Ysusi, 2002. "Measuring and forecasting financial variability using realised variance with and without a model," Economics Papers 2002-W21, Economics Group, Nuffield College, University of Oxford.
    13. 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.
    14. Benjamin Yibin Zhang & Hao Zhou & Haibin Zhu, 2009. "Explaining Credit Default Swap Spreads with the Equity Volatility and Jump Risks of Individual Firms," Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5099-5131, December.
    15. Nour Meddahi, 2001. "A Theoretical Comparison Between Integrated andRealized Volatilities / A Theoretical Comparison Between Integrated and Realized Volatilities," CIRANO Working Papers 2001s-71, CIRANO.
    16. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    17. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    18. Ole E. Barndorff-Nielsen & Svend Erik Graversen & Neil Shephard, 2003. "Power variation & stochastic volatility: a review and some new results," Economics Papers 2003-W19, Economics Group, Nuffield College, University of Oxford.
    19. Elena Andreou & Eric Ghysels, 2004. "Monitoring for Disruptions in Financial Markets," CIRANO Working Papers 2004s-26, CIRANO.
    20. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers 2002-W24, Economics Group, Nuffield College, University of Oxford.

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    Keywords

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

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