Abstracts

Risk premia between spot and forward prices play a key role in energy markets. This paper derives analytic expressions for such risk premia when spot prices are modelled by Levy semistationary (LSS) processes. We find that there is a structural difference between geometric and arithmetic models based on LSS processes. While there is always a stochastic component in the risk premium in a geometric model this is not necessarily true in an arithmetic model. Moreover, we show that when working with a structure-preserving change of measure between the physical and the risk-neutral probability measure, the stochastic volatility is a key component, in particular in the arithmetic model, where it can solely introduce stochastic behaviour in the risk premium. For particular choices of the stochastic volatility process, e.g. for a square-root diffusion or a non-Gaussian Ornstein-Uhlenbeck process, we show how the dynamics of the stochastic volatility process lead to stochastic dynamics of the risk premium.
Electricity is a special case within the class of energy commodities since it is essentially non-storable. We focus on electricity in our empirical work and investigate to what extent the conditional expectation of the average spot price under the physical probability measure has any explanatory power for the corresponding electricity futures. In our empirical study, we focus on the short-end of the forward curve only and use a daily time series of the front months of Phelix Peakload Month Futures from the European Energy Exchange market from Oct 2009 – Sep 2012. Despite the fact that our LSS-based model fits the spot prices very well, we find that the corresponding conditional expectation has only some explanatory power for the futures. There is still a significant amount of variability in the futures which cannot be explained by our predicted average spot prices. Hence, either one models the risk premium directly to find a suitable model for electricity futures or one could model the futures directly. Here we follow the latter approach, where we postulate a model for electricity futures based on the theoretical results obtained for the conditional expectation of the average spot (based on an LSS process). We calibrated such a model directly to the futures and obtained a good model fit.