Joint price and volumetric risk in wind power trading: A copula approach

This paper examines the dependence between wind power production and electricity prices and discusses its implications for the pricing and the risk distributions associated with contracts that are exposed to joint price and volumetric risk. We propose a copula model for the joint behavior of prices and wind power production, which is estimated to data from the Danish power market. We find that the marginal behavior of the individual variables is best described by ARMA–GARCH models with non-Gaussian error distributions, and the preferred copula model is a time-varying Gaussian copula. As an application of our joint model, we consider the case of an energy trading company entering into longer-term agreements with wind power producers, where the fluctuating future wind power production is bought at a predetermined fixed price. We find that assuming independence between prices and wind power production leads to an underestimation of risk, as the profit distribution becomes left-skewed when the negative dependence that we find in the data is accounted for. By performing a simple static hedge in the forward market, we show that the risk can be significantly reduced. Furthermore, an out-of-sample study shows that the choice of copula influences the price of correlation risk, and that time-varying copulas are superior to the constant ones when comparing actual profits generated with different models.