A Note On Emissions Trading: The Pricing Of Carbon Derivatives

Due to extreme volatility in the prices of CO2 permits observed in the European markets, effective hedging techniques such as futures contracts and option instruments rapidly developed, together with approximations to the dynamics of the underlying. To bridge the gap between theory and practice, we are going to devise a market model consistent with the features exhibited by equilibrium models. By definition, the prices of CO2 permits are bounded and so should be their dynamics, so that the spot prices do not have the predictable representation property. Rather than working directly with a bounded process, we model the carbon permits prices as a function of a positive unbounded process, and show that there is no equivalent probability measure such that the discounted spot price is a martingale. Consequently, investors in the emission allowances markets can generate arbitrage opportunities, which explains all the contradictory results recently obtained by various authors to justify the observed discrepancies between the futures and spot prices. Relying on the actuarial pricing approach of marked-to-model, we select freely two particular growth rates for the CO2 spot price process, compute their corresponding dynamics, and rewrite the contingent claims on the carbon spot prices in terms of the unbounded process. As a result, one can define the model of his choice for the unbounded process and compute in a simple way the claims on emission allowances.