A nonlinear diffusion model for electricity prices and derivatives

Abstract

In this paper, we first develop a one-factor diffusion model for electricity prices, which is based on a power transformation of CIR process. We show that the new model is tractable and we are able to derive the analytical solutions for future and future option prices. To enhance the model's ability to capture the prices spikes, we extend it to a time-changed model where the price is modelled by a nonlinear CIR process time changed by Lévy subordinators. We employ the eigenfunction expansion methods to obtain the closed-form solutions for the derivatives. Our empirical study indicates the new models have the potential to capture the main features of electricity data better than the competing models.