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Exact simulation of Ornstein-Uhlenbeck tempered stable processes

Qu, Yan, Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhao, Hongbiao (2021) Exact simulation of Ornstein-Uhlenbeck tempered stable processes. Journal of Applied Probability, 58 (2). 347 - 371. ISSN 0021-9002

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Identification Number: 10.1017/jpr.2020.92


There are two types of tempered stable (TS) based Ornstein–Uhlenbeck (OU) processes: (i) the OU-TS process, the OU process driven by a TS subordinator, and (ii) the TS-OU process, the OU process with TS marginal law. They have various applications in financial engineering and econometrics. In the literature, only the second type under the stationary assumption has an exact simulation algorithm. In this paper we develop a unified approach to exactly simulate both types without the stationary assumption. It is mainly based on the distributional decomposition of stochastic processes with the aid of an acceptance–rejection scheme. As the inverse Gaussian distribution is an important special case of TS distribution, we also provide tailored algorithms for the corresponding OU processes. Numerical experiments and tests are reported to demonstrate the accuracy and effectiveness of our algorithms, and some further extensions are also discussed.

Item Type: Article
Official URL:
Additional Information: © 2021 The Authors
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 Aug 2020 10:54
Last Modified: 13 Jun 2024 23:42

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