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Non-Gaussian OU based models and some of their uses in financial economics

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Ole Barndorff-Nielsen
Neil Shephard

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Abstract

Non-Gaussian processes of Ornstein-Uhlenbeck type, or OU processes for short, offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2000mf01.

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Date of creation: 2000
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Handle: RePEc:sbs:wpsefe:2000mf01

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Web page: http://www.finance.ox.ac.uk
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  1. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508. [Downloadable!]
  2. Marina Resta & Davide Sciutti, . "A characterization of self-affine processes in finance through the scaling function," Modeling, Computing, and Mastering Complexity 2003 13, Society for Computational Economics. [Downloadable!]
  3. Ali Alami & Éric Renault, 2001. "Risque de modèle de volatilité," CIRANO Working Papers 2001s-06, CIRANO. [Downloadable!]
  4. Nour Meddahi, 2002. "ARMA Representation of Integrated and Realized Variances," CIRANO Working Papers 2002s-93, CIRANO. [Downloadable!]
  5. Christian Bontemps & Nour Meddahi, 2002. "Testing Normality: A GMM Approach," CIRANO Working Papers 2002s-63, CIRANO. [Downloadable!]
  6. Torben G. Andersen & Oleg Bondarenko, 2007. "Construction and Interpretation of Model-Free Implied Volatility," NBER Working Papers 13449, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. Siem Jan Koopman & Borus Jungbacker & Eugenie Hol, 2004. "Forecasting Daily Variability of the S&P 100 Stock Index using Historical, Realised and Implied Volatility Measurements," Tinbergen Institute Discussion Papers 04-016/4, Tinbergen Institute. [Downloadable!]
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  8. Nour Meddahi & Éric Renault, 2000. "Temporal Aggregation of Volatility Models," CIRANO Working Papers 2000s-22, CIRANO. [Downloadable!]
  9. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
  10. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 113-124, March. [Downloadable!] (restricted)
  11. Robert Tompkins, 2006. "Why Smiles Exist in Foreign Exchange Options Markets: Isolating Components of the Risk Neutral Process," European Journal of Finance, Taylor and Francis Journals, vol. 12(6-7), pages 583-603, October. [Downloadable!] (restricted)
  12. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO. [Downloadable!]
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  13. Pitt, M.K. & Walker, S.G., 2001. "Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models," The Warwick Economics Research Paper Series (TWERPS) 595, University of Warwick, Department of Economics. [Downloadable!]
  14. Hiroki Masuda, 2005. "Classical Method of Moments for Partially and Discretely Observed Ergodic Models," Statistical Inference for Stochastic Processes, Springer, vol. 8(1), pages 25-50, January. [Downloadable!] (restricted)
  15. Eugenie Hol & Siem Jan Koopman, 2000. "Forecasting the Variability of Stock Index Returns with Stochastic Volatility Models and Implied Volatility," Tinbergen Institute Discussion Papers 00-104/4, Tinbergen Institute. [Downloadable!]
  16. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO. [Downloadable!]
  17. George Tauchen & Hao Zhou, 2006. "Realized jumps on financial markets and predicting credit spreads," Finance and Economics Discussion Series 2006-35, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  18. John Cotter, 2004. "Realized volatility and minimum capital requirements," Money Macro and Finance (MMF) Research Group Conference 2003 20, Money Macro and Finance Research Group. [Downloadable!]
  19. 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. [Downloadable!]
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  20. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  21. Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society. [Downloadable!]
  22. Markku Lanne, 2006. "A Mixture Multiplicative Error Model for Realized Volatility," Economics Working Papers ECO2006/3, European University Institute. [Downloadable!]
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  23. Werker, B. & Meddahi, N. & Renault, E., 2003. "Garch and irregularly spaced data," Discussion Paper 27, Tilburg University, Center for Economic Research. [Downloadable!]
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  24. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO. [Downloadable!]
  25. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2002. "Analytic Evaluation of Volatility Forecasts," CIRANO Working Papers 2002s-90, CIRANO. [Downloadable!]
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