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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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    1. Shibin Zhang & Xinsheng Zhang, 2008. "Exact Simulation of IG-OU Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 337-355, September.
    2. Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010. "Tempered stable and tempered infinitely divisible GARCH models," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2096-2109, September.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    4. T. Pellegrino & P. Sabino, 2015. "Enhancing Least Squares Monte Carlo with diffusion bridges: an application to energy facilities," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 761-772, May.
    5. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
    6. Michele Bianchi & Frank Fabozzi, 2015. "Investigating the Performance of Non-Gaussian Stochastic Intensity Models in the Calibration of Credit Default Swap Spreads," Computational Economics, Springer;Society for Computational Economics, vol. 46(2), pages 243-273, August.
    7. Fred Espen Benth & Luca Di Persio & Silvia Lavagnini, 2018. "Stochastic Modeling of Wind Derivatives in Energy Markets," Risks, MDPI, vol. 6(2), pages 1-21, May.
    8. Cufaro Petroni, Nicola, 2008. "Selfdecomposability and selfsimilarity: A concise primer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 1875-1894.
    9. 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.
    10. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2021. "Correlating Lévy processes with self-decomposability: applications to energy markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1253-1280, December.
    11. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

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    3. 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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