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Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models

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  • Ole E. Barndorff‐Nielsen
  • Neil Shephard

Abstract

. In this paper, we study the detailed distributional properties of integrated non‐Gaussian Ornstein–Uhlenbeck (intOU) processes. Both exact and approximate results are given. We emphasize the study of the tail behaviour of the intOU process. Our results have many potential applications in financial economics, as OU processes are used as models of instantaneous variance in stochastic volatility (SV) models. In this case, an intOU process can be regarded as a model of integrated variance. 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, 2003. "Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(2), pages 277-295, June.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:2:p:277-295
    DOI: 10.1111/1467-9469.00331
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    1. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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