Stochastic differential equation models for the price of European CO₂ emission allowances

Understanding the stochastic nature of emissions allowances is crucial for risk management in emissions trading markets. In this study, we discuss the emissions allowances spot price within the European Union Emissions Trading Scheme: Powernext and European Climate Exchange. To compare the fitness of five stochastic differential equations (SDEs) to the European Union allowances spot price, we apply regression theory to obtain the point and interval estimations for the parameters of the SDEs. An empirical evaluation demonstrates that the mean reverting square root process (MRSRP) has the best fitness of five SDEs to forecast the spot price. To reduce the degree of smog, we develop a new trading scheme in which firms have to hand many more allowances to the government when they emit one unit of air pollution on heavy pollution days, versus one allowance on clean days. Thus, we set up the SDE MRSRP model with Markovian switching to analyse the evolution of the spot price in such a scheme. The analysis shows that the allowances spot price will not jump too much in the new scheme. The findings of this study could contribute to developing a new type of emissions trading.