Description

Pricing Green Financial Products

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 Lévy 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.

1️⃣ Green financial products hedge renewable energy risks (wind power volume & price).
2️⃣ Underlying index: NAREX-WIDE, measuring average wind utilisation vs. capacity.
3️⃣ Deseasonalised wind utilisation follows a CARMA(p,q) stochastic process.
4️⃣ Gaussian vs. Lévy CARMA models capture normal vs. heavy-tailed wind dynamics.
5️⃣ The FEB-Four algorithm links econometrics (CARMA → ARMA) to finance (market price of risk).
6️⃣ Logit transformation and expectile-based variance normalisation (IER/IQR) achieve Gaussian increments.
7️⃣ Risk-neutral pricing derived via Girsanov transform for Brownian or Lévy drivers.
8️⃣ Market price of risk (MPR) estimated from futures data shows seasonal structure.
9️⃣ Negative MPR → producers pay premium to hedge low-wind output; positive → investors pay for stability.
🔟 Gaussian models fit in-sample better, while Lévy CARMA captures extremes and heavy tails.