A rough multi-factor model of electricity spot prices

We introduce a new continuous-time mathematical model of electricity spot prices which accounts for the most important stylized facts of these time series: seasonality, spikes, stochastic volatility, and mean reversion. Empirical studies have found a possible fifth stylized fact, roughness, and our approach explicitly incorporates this into the model of the prices. Our setup generalizes the popular Ornstein–Uhlenbeck-based multi-factor framework of Benth et al. (2007) and allows us to perform statistical tests to distinguish between an Ornstein–Uhlenbeck-based model and a rough model. Further, through the multi-factor approach we account for seasonality and spikes before estimating – and making inference on – the degree of roughness. This is novel in the literature and we present simulation evidence showing that these precautions are crucial for accurate estimation. Lastly, we estimate our model on recent data from six European energy exchanges and find statistical evidence of roughness in five out of six markets. As an application of our model, we show how, in these five markets, a rough component improves short term forecasting of the prices.