Parameter Estimation of Electricity Spot Models from Futures Prices

Abstract

We consider a slight perturbation of the Schwartz-Smith model for the electricity futures prices and the resulting modified spot model. Using the martingale property of the modified price under the risk neutral measure, we derive the arbitrage free model for the spot and futures prices. We estimate the parameters of the model by the method of maximum likelihood using the Kalman filter's estimate of the unobservable state variables, coupled with the usual statistical techniques. The main advantage of the new model is that it avoids the inclusion of artificial noise to the observation equation for the implementation of Kalman filter. The extra noise is build in within the model in an arbitrage free setting.

Filtering and Identification of Stochastic Risk Premium for Electricity Spot Price Models

“…(3) where se(t) denotes the seasonality function. This function is determined a-priori from the historical data by using FFT as used in Aihara et al [2009], Imreizeeq [2011]. For the data shown in Fig.1, the seasonality function is given by se(t) = 0.1526 cos(2π5.5 × 10 −3 t + 2.12) +0.1641 cos(2π8.2 × 10 −3 t − 1.18) +0.1739 cos(2π16.4 × 10 −3 t + 1.36).…”

“…Hence the model parameters can be calibrated through the derived likelihood functional without any ad hoc observation noise. See Aihara et al [2009] for the detailed identification procedure.…”

Parameter estimation of a new energy spot model from futures prices

“…At the end of this chapter, we use simulation and real data of the spot and futures on the UK-Gas-NBP, and establish the feasibility of the proposed filter. This chapter is based on Aihara et al (2009b).…”