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Integrated OU Processes


Author Info

  • Ole E. Barndorff-Nielsen

    (Center for Mathematical Physics and Stochastics (MaPhySto))

  • Neil Shephard

    (Nuffield College, Oxford)


In this paper we study the detailed distributional properties of integrated non-Gaussian OU (intOU) processes. Both exact results and approximate results are given. We emphasise the study of the tail behaviour of the intOU process. Our results have many potential applications in financial economics, for OU processes are used as models of instantaneous volatility in stochastic volatility (SV) models. In this case an intOU process can be regarded as a model of integrated volatility. Hence the tail behaviour of the intOU process will determine the tail behaviour of returns generated by SV models.

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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2001-W1.

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Length: 23 pages
Date of creation: 31 May 2001
Date of revision:
Handle: RePEc:nuf:econwp:0101

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Related research

Keywords: Background driving Levy process; Chronometer; Co-break; Econometrics; Integrated volatility; Kumulant function; Levy density; Option pricing; OU processes; Stochastic volatility;

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  1. 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.
  2. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," NBER Working Papers 7488, National Bureau of Economic Research, Inc.
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Cited by:
  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
  2. Neil Shephard & Ole E. Barndorff-Nielsen, 2001. "Higher order variation and stochastic volatility models," Economics Series Working Papers 2001-W08, University of Oxford, Department of Economics.
  3. James E. Griffin & Mark F.J. Steel, 2002. "Inference With Non-Gaussian Ornstein-Uhlenbeck Processes for Stochastic Volatility," Econometrics 0201002, EconWPA, revised 04 Apr 2003.


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