In this paper, we review the extant mathematical and environmental economics literatures on the stochastic properties of CO
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 function, by Todorov and Tauchen (2010, 2011), our review shows that the Brownian motion shall be dismissed when modelling CO
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 information shocks leading to allowance price jump can be addressed when modelled as an appropriately sampled, centred Lévy or Poisson process.
Keywords: carbon futures, stochastic modelling, jumps, activity signature function