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Power and Bipower Variation with Stochastic Volatility and Jumps

  • Ole E. Barndorff-Nielsen

This article shows that realized power variation and its extension, realized bipower variation, which we introduce here, are somewhat robust to rare jumps. We demonstrate that in special cases, realized bipower variation estimates integrated variance in stochastic volatility models, thus providing a model-free and consistent alternative to realized variance. Its robustness property means that if we have a stochastic volatility plus infrequent jumps process, then the difference between realized variance and realized bipower variation estimates the quadratic variation of the jump component. This seems to be the first method that can separate quadratic variation into its continuous and jump components. Various extensions are given, together with proofs of special cases of these results. Detailed mathematical results are reported in Barndorff-Nielsen and Shephard (2003a). Copyright 2004, Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/jjfinec/nbh001
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Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 2 (2004)
Issue (Month): 1 ()
Pages: 1-37

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Handle: RePEc:oup:jfinec:v:2:y:2004:i:1:p:1-37
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  4. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
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  8. John M. Maheu & Thomas H. McCurdy, 2003. "News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns," CIRANO Working Papers 2003s-38, CIRANO.
  9. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
  10. 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.
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  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  17. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Power Variation and Time Change," Economics Series Working Papers 2002-W24, University of Oxford, Department of Economics.
  18. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  19. 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.
  20. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  21. 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.
  22. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
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