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