Title: A nonlinear diffusion model for electricity prices and derivatives

Authors: Zhigang Tong; Allen Liu

Addresses: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada ' Model Validation, Enterprise Risk and Portfolio Management, Bank of Montreal, First Canadian Place, Toronto, Ontario, M5X 1A3, Canada

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.

Keywords: electricity prices; CIR; OU; constant-elasticity-of-variance; CEV; time change; Lévy subordinators; eigenfunction expansion; derivatives pricing; nonlinear model.

DOI: 10.1504/IJBD.2017.091606

International Journal of Bonds and Derivatives, 2017 Vol.3 No.4, pp.290 - 319

Received: 04 Sep 2017
Accepted: 17 Sep 2017
Published online: 08 May 2018 *

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