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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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  1. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Economics Series Working Papers 2003-W12, University of Oxford, Department of Economics.
  2. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," Working papers 353, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  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.
  5. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  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.
  7. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  8. 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.
  9. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  10. 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-.
  11. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, 04.
  12. G. William Schwert, 1988. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  13. 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.
  14. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Power Variation and Time Change," Economics Series Working Papers 2002-W24, University of Oxford, Department of Economics.
  15. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
  16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  17. 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.
  18. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  19. Andersen, Torben G. & Bollerslev, Tim & Francis X. Diebold,, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," CFS Working Paper Series 2003/35, Center for Financial Studies (CFS).
  20. 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.
  21. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
  22. 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.
  23. 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.
  24. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
  25. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
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