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Power and bipower variation with stochastic volatility and jumps

  • Ole E. Barndorff-Nielsen

    (The Centre for Mathematical Physics and Stochastics (MaPhySto). Univeristy of Aarhus, Denmark)

  • Neil Shephard


    (Department of Economics, and Nuffield College, Oxford University)

This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models --- thus providing a model free and consistent alternative to realised variance. Its robustness property means that if we have an SV plus infrequent jumps process then the difference between realised variance and realised bipower variation estimates the quadratic variation of the jump component. This seems to be the first method which can divide up quadratic variation into its continuous and jump components. Various extensions are given. Proofs of special cases of these results are given. Detailed mathematical results will be reported elsewhere.

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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2003-W17.

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Length: 33 pages
Date of creation: 15 Sep 2003
Date of revision:
Handle: RePEc:nuf:econwp:0318
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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Econometric analysis of realised covariation: high frequency covariance, regression and correlation in financial economics," OFRC Working Papers Series 2002fe03, Oxford Financial Research Centre.
  2. 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.
  3. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
  4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  5. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Power Variation and Time Change," Economics Series Working Papers 2002-W24, University of Oxford, Department of Economics.
  6. 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.
  7. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  8. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  9. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  10. 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.
  11. 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.
  12. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  13. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
  14. 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.
  15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  16. 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.
  17. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
  18. G. William Schwert, 1988. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  19. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  20. 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.
  21. Torben G. Andersen & Tim Bollerslev & 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," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
  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. "Realised power variation and stochastic volatility models," Economics Papers 2001-W18, Economics Group, Nuffield College, University of Oxford.
  24. 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.
  25. 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.
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