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Realised power variation and stochastic volatility models

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  • Neil Shephard
  • Ole E. Barndorff-Nielsen

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 covers, 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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File URL: http://www.nuff.ox.ac.uk/economics/papers/2001/w18/rth_order.pdf
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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 2001-W18.

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Date of creation: 01 Jun 2002
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Handle: RePEc:oxf:wpaper:2001-w18

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Web page: http://www.economics.ox.ac.uk/
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Related research

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

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  1. Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, American Finance Association, vol. 50(2), pages 507-28, June.
  2. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  3. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(4), pages 317-340, December.
  4. Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers, CIRANO 2000s-22, CIRANO.
  5. Fulvio Corsi & Gilles Zumbach & Ulrich Müller & Michel Dacorogna, 2004. "Consistent high-precision volatility from high-frequency data," Finance, EconWPA 0407005, EconWPA.
  6. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, Elsevier, vol. 4(2-3), pages 115-158, June.
  7. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  8. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
  9. John Galbraith & Victoria Zinde-Walsh, 2001. "Properties of Estimates of Daily GARCH Parameters Basaed on Intra-Day Observations," CIRANO Working Papers, CIRANO 2001s-15, CIRANO.
  10. 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.
  11. West, Kenneth D. & Cho, Dongchul, 1995. "The predictive ability of several models of exchange rate volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 69(2), pages 367-391, October.
  12. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.
  13. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2001-49, Board of Governors of the Federal Reserve System (U.S.).
  14. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  15. Cao, C Q & Tsay, R S, 1992. "Nonlinear Time-Series Analysis of Stock Volatilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 7(S), pages S165-85, Suppl. De.
  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. 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.
  18. 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.
  19. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, Elsevier, vol. 1(1), pages 83-106, June.
  20. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  21. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 50(2), pages 125-150, November.
  22. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers, CIRANO 2000s-19, CIRANO.
  23. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "How accurate is the asymptotic approximation to the distribution of realised volatility?," Economics Papers 2001-W16, Economics Group, Nuffield College, University of Oxford.
  24. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
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