Stochastic modeling of the spot price of electricity incorporating commodities and renewables as exogenous factors

Models for electricity spot prices are used for a variety of valuation issues, e.g. pricing of (real) options and pricing on the retail market. These issues require adequate stochastic price models. A major requirement is the reproduction of stylized facts of the spot price of electricity. Furthermore, the dependencies on other commodities need to be modeled as well. Combined models of all relevant commodities gain importance in the context of risk management of energy utilities. The complexity of options and of portfolios of energy utilities increases due to the number of products with multiple commodities included. This makes the use of combined models essential.

The spot price of electricity is set by the principle of merit order. The most important drivers for the merit order curve on the EEX market are grid load, generation of renewables and prices of coal, natural gas, oil and emission allowances. We present a model incorporating these influence factors in a functional approximation of the non-deterministic merit order curve. The stylized facts mean reversion, seasonalities, negative prices and price spikes as observable in historical spot prices are reproduced.

The input factors require models as well. The residual load model relies on distinct models for renewables including their increase and grid load. We introduce a gas price model incorporating temperature and oil price as exogenous factors. Three model alternatives are presented for the considered commodity prices. A comparison gives evidence that the cointegration approach describes the dependencies best. Finally, the electricity price model is applied to risk-adequate pricing on the retail market.