With increasing wind power (WP) penetration an extensive amount of volatile and weather dependent energy is fed into the German electricity system. To manage the volume risk of windless days and the transfer of revenue risk from wind turbine owners to investors, WP derivatives were introduced. These insurance-like securities allow the hedging of the volume risk of unstable WP production on exchanges such as NASDAQ and EEX. We present a modern and powerful methodology to model weather derivatives, with very skewed underlying assets, incorporating techniques from extreme event modelling to tune seasonal volatility. We compare transformed Gaussian and non-Gaussian CARMA(p, q) models. Our results indicate that the Gaussian CARMA(p, q) model is preferred over the non-Gaussian alternative. Out-of-sample backtesting results show good performance, with respect to benchmarks, employing smooth market price of risk (MPR) estimates based on NASDAQ weekly and monthly German WP futures prices. A seasonal MPR of a smile shape is observed, with slightly positive values in times of high volatility, for example, winter months, and negative values, in times of low volatility and production, for example, in summer months. We conclude that producers pay premiums to insure stable revenue steams, while investors pay premiums when weather risk is high.

中文翻译：

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风电期货定价

随着风力发电 (WP) 渗透率的提高，大量不稳定且依赖天气的能源被输送到德国电力系统中。为了管理无风天的体积风险以及将收益风险从风力涡轮机所有者转移到投资者，引入了可湿性粉剂衍生品。这些类似保险的证券可以对冲纳斯达克和 EEX 等交易所不稳定 WP 生产的数量风险。我们提出了一种现代而强大的方法来模拟天气衍生品，具有非常倾斜的基础资产，结合极端事件建模技术来调整季节性波动。我们比较了转换后的高斯和非高斯 CARMA( p ,  q ) 模型。我们的结果表明高斯 CARMA( p ,  q) 模型优于非高斯替代方案。样本外回测结果显示，相对于基准而言，表现良好，采用基于 NASDAQ 每周和每月德国 WP 期货价格的平滑市场风险价格 (MPR) 估计。观察到微笑形状的季节性 MPR，在高波动时期（例如冬季）具有略微正值，在低波动和生产时期（例如在夏季）具有负值。我们得出的结论是，生产商支付溢价以确保稳定的收入流，而投资者在天气风险高时支付溢价。