Wind is considered to be a free, renewable and environmentally friendly source of energy. However, wind farms are exposed to excessive weather risk since the power production depends on the wind speed, the wind direction and the wind duration. This risk can be successfully hedged using a ?nancial instrument called weather derivatives. In this study the dynamics of the wind generating process are modeled using a non-parametric non-linear wavelet network. Our model is validated in New York. The proposed methodology is compared against alternative methods, proposed in prior studies. Our results indicate that wavelet networks can model the wind process very well and consequently they constitute an accurate and ef?cient tool for wind derivatives pricing. Finally, we provide the pricing equations for wind futures written on two indices, the cumulative average wind speed index and the Nordix wind speed index.

Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications.

In this paper, we use wavelet neural networks in order to model a mean-reverting Ornstein–Uhlenbeck temperature process, with seasonality in the level and volatility and time-varying speed of mean reversion. We forecast up to 2 months ahead out of sample daily temperatures, and we simulate the corresponding Cumulative Average Temperature and Heating Degree Day indices. The proposed model is validated in 8 European and 5 USA cities all traded in the Chicago Mercantile Exchange. Our results suggest that the proposed method outperforms alternative pricing methods, proposed in prior studies, in most cases. We find that wavelet networks can model the temperature process very well and consequently they constitute an accurate and efficient tool for weather derivatives pricing. Finally, we provide the pricing equations for temperature futures on Cooling and Heating Degree Day indices.

In this paper, we use neural networks in order to model the seasonal component of the residual variance of a mean-reverting Ornstein–Uhlenbeck temperature process, with seasonality in the level and volatility. This approach can be easily used for pricing weather derivatives by performing Monte Carlo simulations. Moreover, in synergy with neural networks we use wavelet analysis to identify the seasonality component in the temperature process as well as in the volatility of the temperature anomalies. Our model is validated on more than 100 years of data collected from Paris, one of the European cities traded at Chicago Mercantile Exchange. Our results show a significant improvement over more traditional alternatives, regarding the statistical properties of the temperature process. This is important since small misspecifications in the temperature process can lead to large pricing errors.

In this paper, in the context of an Ornstein-Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter ? of the process. We estimate non-parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for ?. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of ?, and no seasonal patterns. This is important, since in all relevant studies performed thus far, ? was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where ? is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when ? is time dependent.