Valuation of carbon emission allowance options under an open trading phase

This paper presents valuation models of emission allowance options under an emission trading scheme, operating in an open trading phase, where unused allowances are banked to subsequent phases without any limit. Empirical studies are carried out to show that allowance option prices exhibit similar volatility smiles to those of the stock market. Three reduced-form econometrics models, namely a Lognormal allowance price model, a Skewness–Kurtosis-Modified Lognormal allowance price model, and a Mixture Lognormal allowance price model are introduced, with each being accorded with a rich interpretation of its own. Numerical illustration of the models is performed through calibration to the European-Union Emission-Trading-Scheme’s allowance futures option prices collected for EU ETS Phase 3 and Phase 4 respectively, where statistical fitness of the models is assessed comparatively within each sample and across the two samples collected to ensure robustness of the conclusions.