Stochastic Volatility Modeling of Emission Allowances Futures Prices in the European Union Emission Trading System Market

Abstract

We conduct an empirical investigation of the logreturns of the futures prices of the European Union Emission Trading System emission certificates traded in the Nord Pool market between 2005 and 2013. We observe heaviness, skewness, and high kurtosis of these logreturns. We thus propose modeling the futures logprices using the Barndorff-Nielsen and Shephard (BNS) or the Heston stochastic volatility models.We carry out an empirical comparison between the performances of these models and investigate their stationary autocorrelation structure. In particular, as a consequence of allowing for skewness in the Heston model, we find analytical expressions for the autocorrelation function of the logreturns and their squares. Our analysis indicates the presence of short-range dependence in the observed futures logprice returns. We conclude that the BNS model better describes the empirical features of the observed futures prices than the Heston model. Our findings have relevance for the real option modeling of fossil-fueled power plants when considering emission costs.