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Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of $$\hbox {CO}_2$$ CO 2 and fuel-switching

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  • Julien Chevallier

    () (IPAG Business School (IPAG Lab)
    Université Paris 8 (LED))

  • Stéphane Goutte

    (Université Paris 8 (LED)
    Paris School of Business (PSB))

Abstract

Abstract This paper proposes an estimation methodology for Lévy-driven Ornstein–Uhlenbeck processes. The estimation unfolds in two steps, with a least-squares method for a subset of parameters in the first stage, and a constrained maximum likelihood for the remaining diffusion and Lévy distribution parameters. We develop this estimation procedure to demonstrate that the class of mean-reverting Lévy jump processes provides a better fit of the electricity and $$\hbox {CO}_2$$ CO 2 (carbon) market prices. In particular, we describe the dynamics of the fuel-switching price (from coal to gas) when taking into account carbon costs. Several stochastic processes are considered to model the fuel-switching price: (1) the Brownian motion, and (2) Poisson and a panel of Lévy jump processes. The results unambiguously point out the need to resort to jump modeling techniques to model satisfactorily the fuel-switching price. The Gaussianity assumption is also clearly rejected in favor of jump models, especially for pure-jump processes such as Lévy processes.

Suggested Citation

  • Julien Chevallier & Stéphane Goutte, 2017. "Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of $$\hbox {CO}_2$$ CO 2 and fuel-switching," Annals of Operations Research, Springer, vol. 255(1), pages 169-197, August.
  • Handle: RePEc:spr:annopr:v:255:y:2017:i:1:d:10.1007_s10479-015-1967-5
    DOI: 10.1007/s10479-015-1967-5
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    Cited by:

    1. Asante Gyamerah, Samuel & Ngare, Philip & Ikpe, Dennis, 2018. "A Levy Regime-Switching Temperature Dynamics Model for Weather Derivatives," MPRA Paper 89680, University Library of Munich, Germany, revised 10 Jul 2018.
    2. Samuel Asante Gyamerah & Philip Ngare & Dennis Ikpe, 2018. "Regime-Switching Temperature Dynamics Model for Weather Derivatives," Papers 1808.04710, arXiv.org.

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