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Electricity load forecasts are an integral part of many decision-making processes in the electricity market. However, most literature on electricity load forecasting concentrates on deterministic forecasts, neglecting possibly important information about uncertainty. A more complete picture of future demand can be obtained by using distributional forecasts, allowing for a more efficient decision-making. A predictive density can be fully characterized by tail measures such as quantiles and expectiles. Furthermore, interest often lies in the accurate estimation of tail events rather than in the mean or median. We propose a new methodology to obtain probabilistic forecasts of electricity load, that is based on functional data analysis of generalized quantile curves. The core of the methodology is dimension reduction based on functional principal components of tail curves with dependence structure. The approach has several advantages, such as flexible inclusion of explanatory variables including meteorological forecasts and no distributional assumptions. The methodology is applied to load data from a transmission system operator (TSO) and a balancing unit in Germany. Our forecast method is evaluated against other models including the TSO forecast model. It outperforms them in terms of mean absolute percentage error (MAPE) and achieves a MAPE of 2:7% for the TSO. more...

We analyze a consistent two-factor model for pricing temperature derivatives that incorporates the forward looking information available in the market by specifying a model for the dynamics of the complete meteorological forecast curve. The two-factor model is a generalization of the Nelson-Siegel curve model by allowing factors with mean-reversion to a stochastic mean for structural changes and seasonality for periodic patterns. Based on the outcomes of a statistical analysis of forecast data we conclude that the two-factor model captures well the stylized features of temperature forecast curves. In particular, a functional principal component analysis reveals that the model re ects reasonably well the dynamical structure of forecast curves by decomposing their shapes into a tilting and a bending factor. We continue by developing an estimation procedure for the model, before we derive explicit prices for temperature derivatives and calibrate the market price of risk (MPR) from temperature futures derivatives (CAT, HDD, CDD) traded at the Chicago Mercantile Exchange (CME). The factor model shows that the behavior of the implied MPR for futures traded in and out of the measurement period is more stable than other estimates obtained in the literature. This con rms that at least parts of the irregularity of the MPR is not due to irregular risk perception but rather due to information misspecification. Similar to temperature derivatives, this approach can be used for pricing other non-tradable assets. more...

We analyse the short-term spot price of European Union Allowances (EUAs), which is of particular importance in the transition of energy markets and for the development of new risk management strategies. Due to the characteristics of the price process, such as volatility persistence, breaks in the volatility process and heavy-tailed distributions, we investigate the use of Markov switching GARCH (MS-GARCH) models on daily spot market data from the second trading period of the EU ETS. Emphasis is given to short-term forecasting of prices and volatility. We find that MS-GARCH models distinguish well between two states and that the volatility processes in the states are clearly different. This finding can be explained by the EU ETS design. Our results support the use of MS-GARCH models for risk management, especially because their forecasting ability is better than other Markov switching or simple GARCH models. more...

In this paper we investigate price and volatility risk originating in linkages between energy and agricultural commodity prices in Germany and study their dynamics over time. We propose an econometric approach to quantify the volatility and correlation risk structure, which has a large impact for investment and hedging strategies of market participants as well as for policy makers. Volatilities and their short and long run linkages (spillovers) are analyzed using a dynamic conditional correlation GARCH model as well as a multivariate multiplicative volatility model. Our approach provides a flexible and accurate fitting procedure for volatility and correlation risk. more...

Many business people such as farmers and financial investors are affected by indirect losses caused by scarce or abundant rainfall. Because of the high potential of insuring rainfall risk, the Chicago Mercantile Exchange (CME) began trading rainfall derivatives in 2011. Compared to temperature derivatives, however, pricing rainfall derivatives is more difficult. In this article, we propose to model rainfall indices via a flexible type of distribution, namely the normal-inverse Gaussian distribution, which captures asymmetries and heavy-tail behaviour. The prices of rainfall futures are computed by employing the Esscher transform, a wellknown tool in actuarial science. This approach is flexible enough to price any rainfall contract and to adjust theoretical prices to market prices by using the calibrated market price of risk. This empirical analysis is conducted with U.S. precipitation data and CME futures data providing first results on the market price of risk for rainfall derivatives. more...

Recently the topic of global warming has become very popular. The literature has concentrated its attention on the evidence of such effect, either by detecting regime shifts or change points in time series. The majority of these methods are designed to find shifts in mean, but only few can do this for the variance. In this paper we attempt to investigate the statistical evidence of global warming by identifying shifts in seasonal mean of daily average temperatures over time and in seasonal variance of temperature residuals. We present a time series approach for modelling temperature dynamics. A seasonal mean Lasso-type technique based with a multiplicative structure of Fourier and GARCH terms in volatility is proposed. The model describes well the stylised facts of temperature: seasonality, intertemporal correlations and the heteroscedastic behaviour of residuals. The application to European temperature data indicates that the multiplicative model for the seasonal variance performs better in terms of out of sample forecast than other models proposed in the literature for modelling temperature dynamics. We study the dynamics of the seasonal variance by implementing quantile and expectile functions with confidence corridor to detrended and deseasonalized residuals. We show that shifts in seasonal mean and variance vary from location to location, indicating that all sources of trends other than mean and variance would rise trends over spatial scales. The local effects of temperature risk support the existence of global warming. more...

Forecasting based pricing of Weather Derivatives (WDs) is a new approach in valuation of contingent claims on nontradable underlyings. Standard techniques are based on historical weather data. Forward-looking information such as meteorological forecasts or the implied market price of risk (MPR) are often not incorporated. We adopt a risk neutral approach (for each location) that allows the incorporation of meteorological forecasts in the framework of WD pricing. We study weather Risk Premiums (RPs) implied from either the information MPR gain or the meteorological forecasts. The size of RPs is interesting for investors and issuers of weather contracts to take advantages of geographic diversification, hedging effects and price determinations. By conducting an empirical analysis to London and Rome WD data traded at the Chicago Mercantile Exchange (CME), we find out that either incorporating the MPR or the forecast outperforms the standard pricing techniques. more...

Weather derivatives (WD) are different from most financial derivatives because the underlying weather cannot be traded and therefore cannot be replicated by other financial instruments. The market price of risk (MPR) is an important parameter of the associated equivalent martingale measures used to price and hedge weather futures/options in the market. The majority of papers so far have priced non-tradable assets assuming zero MPR, but this assumption underestimates WD prices. We study the MPR structure as a time dependent object with concentration on emerging markets in Asia. We find that Asian Temperatures (Tokyo, Osaka, Beijing, Teipei) are normal in the sense that the driving stochastics are close to a Wiener Process. The regression residuals of the temperature show a clear seasonal variation and the volatility term structure of CAT temperature futures presents a modified Samuelson effect. In order to achieve normality in standardized residuals, the seasonal variation is calibrated with a combination of a fourier truncated series with a GARCH model and with a local linear regression. By calibrating model prices, we implied the MPR from Cumulative total of 24-hour average temperature futures (C24AT) for Japanese Cities, or by knowing the formal dependence of MPR on seasonal variation, we price derivatives for Kaohsiung, where weather derivative market does not exist. The findings support theoretical results of reverse relation between MPR and seasonal variation of temperature process. more...