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Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps

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  • Yan Qu
  • Angelos Dassios
  • Hongbiao Zhao

Abstract

We develop a distributional decomposition approach for exactly simulating two types of Gamma-driven Ornstein–Uhlenbeck (OU) processes with time-varying marginal distributions: the Gamma-OU process and the OU-Gamma process. The former has finite-activity jumps, and its marginal distribution is asymptotically Gamma; the latter has infinite-activity jumps that are driven by a Gamma process. We prove that the transition distributions of the two processes at any given time can be exactly decomposed into simple elements: at any given time, the former is equal in distribution to the sum of one deterministic trend and one compound Poisson random variable (r.v.); the latter is equal in distribution to the sum of one deterministic trend, one compound Poisson r.v., and one Gamma r.v. The results immediately lead to very efficient algorithms for their exact simulations without numerical inversion. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms.

Suggested Citation

  • Yan Qu & Angelos Dassios & Hongbiao Zhao, 2021. "Exact simulation of gamma-driven Ornstein–Uhlenbeck processes with finite and infinite activity jumps," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(2), pages 471-484, February.
    • Handle: RePEc:taf:tjorxx:v:72:y:2021:i:2:p:471-484
    DOI: 10.1080/01605682.2019.1657368
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    Cited by:

    1. Yan Qu & Angelos Dassios & Hongbiao Zhao, 2023. "Shot-noise cojumps: Exact simulation and option pricing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 647-665, March.
    2. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    3. Tim Leung & Kevin W. Lu, 2023. "Monte Carlo Simulation for Trading Under a L\'evy-Driven Mean-Reverting Framework," Papers 2309.05512, arXiv.org, revised Jan 2024.
    4. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.

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