Modeling Spikes, Heavy-Tails, and Volatility Clustering in Electricity by Applying a Stochastic Time-Change to the Ornstein-Uhlenbeck Process

Abstract

We present a continuous-time model that applies a stochastic time-change to the Ornstein-Uhlenbeck process for capturing mean-reversion, spikes, heavy-tailed returns, and volatility clustering observed in the daily PJM electricity spot prices. We prove that all moments of the time-changed process exist and have exact analytical solutions, making model calibration possible through the method of moments. We also conduct simulation analysis and nd that the model generates returns that are more heavy-tailed than empirically observed, and thus is not particularly suitable for modeling the PJM data.