Abstract: With increasing wind power penetration more and more volatile and weather dependent energy is fed into the German electricity system. To manage the risk of windless days and transfer revenue risk from wind turbine owners to investors wind power derivatives were introduced. These insurance-like securities (ILS) allow to hedge the risk of unstable wind power production on exchanges like Nasdaq and European Energy Exchange. These products have been priced before using risk neutral pricing techniques. We present a modern and powerful methodology to model weather derivatives with very skewed underlyings incorporating techniques from extreme event modelling to tune seasonal volatility and compare transformed Gaussian and non-Gaussian CARMA(p; q) models. Our results indicate that the transformed Gaussian CARMA(p; q) model is preferred over the non-Gaussian alternative with LÚvy increments. Out-of-sample backtesting results show good performance wrt burn analysis employing smooth Market Price of Risk (MPR) estimates based on NASDAQ weekly and monthly German wind power futures prices and German wind power utilisation as underlying. A seasonal MPR of a smile-shape is observed, with positive values in times of high volatility, e.g. winter months, and negative values, in times of low volatility and production, e.g. in summer months. We conclude that producers pay premiums to insure stable revenue steams, while investors pay premiums when weather risk is high.

Key Words: market price of risk, risk premium, renewable energy, wind power futures, stochastic process, expectile, CARMA, jump, LÚvy, transform, logit-normal, extreme.