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

Julien Chevallier and Stéphane Goutte ()

Annals of Operations Research, 2017, vol. 255, issue 1, No 10, 169-197

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.

Keywords: Stochastic processes; OR in energy; Lévy process; Normal inverse Gaussian; $$\hbox {CO}_2$$ CO 2; Fuel-switching; C15; C53; Q40; 60G51; 60H35; 91G70 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10479-015-1967-5

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