Calibration of electricity price models

Abstract

This paper addresses the issue of model calibration to electricity prices. The non-storability of electricity introduces new problems in terms of modeling and calibration, especially when the objective is to represent both spot prices and forward products, the latter showing a particular time interval: the delivery period. The two main approaches to model electricity prices are: (i) models on a fictitious forward curve from what we can deduce spot prices and forward products with any delivery period, and (ii) models on spot prices from what we can deduce any forward products. In this paper we study both approaches and we focus on the calibration issues. The first part of the paper studies different calibration methods for a classic Gaussian factorial model as described in Benth and Koekebakker (2008), Kiesel, Schidlmayr, and Börger (2009) and mostly based on Heath-Jarrow-Morton approach (Heath, Jarrow, and Morton, Econometrica, 1992). In this case different calibration methods can be proposed, based on spot and/or forward prices, but the main objective is to compare or validate these estimation procedures. We compare these procedures on the valuation of specific portfolios and we then stress the high impact of the calibration method. The second part concerns the calibration issues of a structural model proposed in Aïd, Campi, Langrené (2013). In particular we study the reconstruction performances of forward prices and we address the issue of model calibration in terms of determining the parameters to exactly fit the observable forward products. We propose a modification in the structural model to ensure its ability to be calibrated on all the observed forward products and we give some illustrations of calibration performances.