Abstract
The recent liberalization of electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this article, we jointly model gas and electricity spot prices using a mean-reverting model that fits the correlation structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions that captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then we simulate some trajectories that reproduce well the observed prices behaviour. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio.
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