Review of the Stochastic Properties of CO2 Futures Prices

In this paper, we review the extant mathematical and environmental economics literatures on the stochastic properties of CO2 emission allowance futures prices. We explain the main findings arising from this literature from both continuous- and jump-diffusion models. Based on the Activity Signature Fuction by Todorov and Tauchen (2010,2011), our review shows that the Brownian motion shall be dismissed when modeling CO2 futures, in sharp contrast with the bulk of previous literature on this topic. The central result is that the evolution of the carbon futures price can be described in terms of a pure jump-diffusion process. For instance, important cases of informational shocks leading to allowance price jump can be addressed when modeled as an appropriately sampled, centered Lévy or Poisson process.