Levy process-driven mean-reverting electricity price model: the marginal distribution analysis

We propose a class of stochastic mean-reverting models for electricity prices with Levy process-driven Ornstein-Uhlenbeck (OU) processes being the building blocks. We first fit marginal distributions of power price series to two special classes of distributions defined by quantile functions (termed Class I and Class II distributions). A theoretical correlation structure is then used to fit the empirical autocorrelation structure. Lastly, based on results from the first two steps, we construct a stochastic process by superposing two OU processes. The focus of this paper is on fitting the marginal distribution. A Class I distribution has closed-form formulas for probability density, cumulative distribution function, and quantile function, while a Class II distribution may have extremely unbalanced tails. Both classes of distributions admit realistic modelling of the marginal distribution of electricity prices. This approach effectively captures not only the anomalous tail behaviors but also the correlation structure present in the electricity price series.