Optimal hedging in European electricity forward markets.

This article is concerned with modeling the dynamic and distributional properties of daily spot and forward electricity prices across European wholesale markets. Prices for forward contracts are extracted from a unique database from a major energy trader in Europe. Spot and forward returns are found to be highly non normally distributed. Alternative densities provide a better fit of data. In all cases, conditional heteroscedastic models are used with success to specify the data generating process of returns. We derive implications from the relation between spot and forward prices for the evaluation of hedging effectiveness of bilateral contracts. The relation is parametrized by the mean of multivariate GARCH models possibly allowing for dynamic conditional correlation. Because correlation between spot and forward returns is very low on each market, derived optimal hedge ratios are insignificant. We conclude to a great inefficiency for forward markets at least for short-term horizon. Hedging effectiveness is not improved, for our data, through the use of dynamic correlation models.Electricity; multivariate GARCH; dynamic correlation models; non Gaussian densities; optimal hedging; cross-hedging;

Weather forecasting for weather derivatives : [revised version: January 2, 2004]

We take a simple time-series approach to modeling and forecasting daily average temperature in U.S. cities, and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market. The answer is, perhaps surprisingly, yes. Time-series modeling reveals conditional mean dynamics, and crucially, strong conditional variance dynamics, in daily average temperature, and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises. As we argue, it also holds promise for producing the long-horizon predictive densities crucial for pricing weather derivatives, so that additional inquiry into time-series weather forecasting methods will likely prove useful in weather derivatives contexts

Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matrices

It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common that over-simplistic assumptions will be made. In particular, in order to generate the large covariance matrices that are used in Value-at-Risk models, some very strong constraints are imposed on the movements in volatility and correlations in all the standard models. The constant volatility assumption is also imposed, because it has not been possible to generate large GARCH covariance matrices with mean-reverting term structures.