Estimation of Lévy-driven Ornstein-Ulhenbeck processes: Application to modeling of CO2 and fuel-switching

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 CO2 (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: (i) the Brownian
motion, and (ii) 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.