Estimation of Lévy-driven Ornstein‐Uhlenbeck 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 ${\text{CO}}_2$ (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.