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Fast simulation of tempered stable Ornstein–Uhlenbeck processes

Author

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  • Piergiacomo Sabino

    (Quantitative Risk Management
    University of Helsinki)

  • Nicola Cufaro Petroni

    (Università di Bari INFN Sezione di Bari)

Abstract

Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the a-remainder of their self-decomposable stationary laws. In the present study we fully characterize the Lévy triplet of these $$a$$ a -remainders and we provide a general framework to deduce the transition laws of the finite variation Ornstein–Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein–Uhlenbeck processes related to such distributions, with the further advantage of adopting procedures which are tens of times faster than those already available in the existing literature.

Suggested Citation

  • Piergiacomo Sabino & Nicola Cufaro Petroni, 2022. "Fast simulation of tempered stable Ornstein–Uhlenbeck processes," Computational Statistics, Springer, vol. 37(5), pages 2517-2551, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01205-8
    DOI: 10.1007/s00180-022-01205-8
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    References listed on IDEAS

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    Cited by:

    1. Takuji Arai & Yuto Imai, 2024. "Option pricing for Barndorff-Nielsen and Shephard model by supervised deep learning," Papers 2402.00445, arXiv.org.
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    3. Arai, Takuji & Imai, Yuto, 2024. "Monte Carlo simulation for Barndorff–Nielsen and Shephard model under change of measure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 223-234.
    4. Takuji Arai & Yuto Imai, 2023. "Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure," Papers 2306.05750, arXiv.org.

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