The valuation of futures options for emissions allowances under the term structure of stochastic multi-factors

We develop the general model of the futures options valuation under the term structure of stochastic multi factors. Our model analysis suggest the futures options function carry information about the volatility and adjustment speed of arbitrary multi factors, the correlation among multi-factors, and the time to maturity of futures and options contract. We provide numerical examples compare their difference between the actual and theoretical futures options valuation. Our empirical results show the term structure of arbitrary multi factors has significant effect on the futures options valuation for CO ₂ emissions allowances, we can estimate the theoretical futures options valuation by using historical market information. We can determine the reasonable options price for CO₂ emissions allowances and then make right options trading policy in the emissions allowances options markets.