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Integrated OU Processes and Non‐Gaussian OU‐based Stochastic Volatility Models
Author(s) -
BarndorffNielsen Ole E.,
Shephard Neil
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00331
Subject(s) - stochastic volatility , mathematics , econometrics , volatility (finance) , ornstein–uhlenbeck process , gaussian process , variance (accounting) , gaussian , realized variance , stochastic process , statistical physics , statistics , economics , physics , accounting , quantum mechanics
. 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.