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

Abstract

This paper proposes an estimation methodology for Levy-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 Levy distribution parameters. We develop this estimation procedure to demonstrate that the class of mean-reverting Levy jump processes provides a better fit of the electricity and \(\hbox {CO}_2\) (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 Levy 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 Levy processes.