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Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives

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  • Piergiacomo Sabino

Abstract

In this study we define a three-step procedure to relate the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the law of the increments of such processes. Based on this procedure and the results of Qu et al. (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma, and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins et al. (2017, 2018).

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  • Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.
    • Handle: RePEc:arx:papers:2004.06786
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    Cited by:

    1. 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.
    2. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2020. "A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets," Papers 2011.04256, arXiv.org.
    3. 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.
    4. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    5. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    6. Piergiacomo Sabino, 2021. "Normal Tempered Stable Processes and the Pricing of Energy Derivatives," Papers 2105.03071, arXiv.org.
    7. Roberto Baviera & Pietro Manzoni, 2024. "Fast and General Simulation of L\'evy-driven OU processes for Energy Derivatives," Papers 2401.15483, arXiv.org.

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