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Integrated OU Processes

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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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  • Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Integrated OU Processes," Economics Papers 2001-W1, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:0101
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    File URL: http://www.nuff.ox.ac.uk/Economics/papers/2001/w1/intou1.pdf
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    1. 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-.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 159-179, September.
    3. 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.
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    Cited by:

    1. Wim Schoutens & Stijn Symens, 2003. "The Pricing Of Exotic Options By Monte–Carlo Simulations In A Lévy Market With Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(08), pages 839-864.
    2. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Higher order variation and stochastic volatility models," Economics Papers 2001-W8, Economics Group, Nuffield College, University of Oxford.
    4. Neil Shephard & Ole E. Barndorff-Nielsen & University of Aarhus, 2001. "Normal Modified Stable Processes," Economics Series Working Papers 72, University of Oxford, Department of Economics.

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