Title: Review of the stochastic properties of CO₂ futures prices

Authors: Julien Chevallier

Addresses: IPAG Business School (IPAG Lab), 184 Boulevard Saint-Germain, 75006 Paris, France

Abstract: 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 function, by Todorov and Tauchen (2010, 2011), our review shows that the Brownian motion shall be dismissed when modelling 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 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; mathematical economics; environmental economics; futures prices; carbon dioxide; CO2; Brownian motion; modelling; jump diffusion.

DOI: 10.1504/IJGEI.2013.065185

International Journal of Global Energy Issues, 2013 Vol.36 No.5/6, pp.312 - 328

Accepted: 12 Jul 2014
Published online: 21 Nov 2014 *

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