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Power and bipower variation with stochastic volatility and jumps

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  • 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)

Abstract

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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2003/W18/eric_may03.pdf
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Bibliographic Info

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

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  1. 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, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
  2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
  3. 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, Elsevier, vol. 131(1-2), pages 217-252.
  4. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," NBER Working Papers 1462, National Bureau of Economic Research, Inc.
  5. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers, Duke University, Department of Economics 02-03, Duke University, Department of Economics.
  6. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, Springer, vol. 2(1), pages 41-68.
  7. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers, Economics Group, Nuffield College, University of Oxford 146, Economics Group, Nuffield College, University of Oxford.
  8. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers, Economics Group, Nuffield College, University of Oxford 2005-W17, Economics Group, Nuffield College, University of Oxford.
  9. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-49, CIRANO.
  10. Elena Andreou & Eric Ghysels, 2004. "The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests," CIRANO Working Papers, CIRANO 2004s-25, CIRANO.
  11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  12. 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, Oxford Financial Research Centre 2002fe03, Oxford Financial Research Centre.
  13. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  14. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, American Finance Association, vol. 44(5), pages 1115-53, December.
  15. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers, Economics Group, Nuffield College, University of Oxford 1997-W13, Economics Group, Nuffield College, University of Oxford.
  16. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 579-625, March.
  17. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Power Variation and Time Change," Economics Papers, Economics Group, Nuffield College, University of Oxford 2002-W24, Economics Group, Nuffield College, University of Oxford.
  18. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  19. 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, Royal Statistical Society, vol. 64(2), pages 253-280.
  20. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  21. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 281-316, June.
  22. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Realised power variation and stochastic volatility models," Economics Series Working Papers, University of Oxford, Department of Economics 2001-W18, University of Oxford, Department of Economics.
  23. 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, Oxford Financial Research Centre 2002mf05, Oxford Financial Research Centre.
  24. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 59(2), pages 755-793, 04.
  25. 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, Royal Statistical Society, vol. 63(2), pages 167-241.
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