A space-time random field model for electricity forward prices

Abstract

Stochastic models for forward electricity prices are of great relevance nowadays, given the major structural changes in the market due to the increase of renewable energy in the production mix. In this study, we derive a spatio-temporal dynamical model based on the Heath-Jarrow-Morton (HJM) approach under the Musiela parametrization, which ensures an arbitrage-free model for electricity forward prices. The model is fitted to a unique data set of historical price forward curves. As a particular feature of the model, we disentangle the temporal from spatial (maturity) effects on the dynamics of forward prices, and shed light on the statistical properties of risk premia, of the noise volatility term structure and of the spatio-temporal noise correlation structures. We find that the short-term risk premia oscillates around zero, but becomes negative in the long run. We identify the Samuelson effect in the volatility term structure and volatility bumps, explained by market fundamentals. Furthermore we find evidence for coloured noise and correlated residuals, which we model by a Hilbert space-valued normal inverse Gaussian Lévy process with a suitable covariance functional.

A survey of electricity spot and futures price models for risk management applications

“…They are mainly interested in the estimation of the parameters and the number of factors that are done by using futures price data in an independent component analysis. In an even more general framework, Barth and Benth [14] and Benth and Paraschiv [31] model futures prices using random fields that can be likened to an infinite number of factors. The space dimension is time to maturity and is related to the Musiela parameterization.…”

Sensitivity analysis in the infinite dimensional Heston model

“…[4]) and also signs of non-Gaussianity (see e.g. [6]). We choose to consider the Heston-type infinite dimensional volatility model proposed in [5], and study both the pricing of options written on the forwards and provide tools for the sensitivity analysis.…”

Short- to Mid-term Day-Ahead Electricity Price Forecasting Using Futures

“…For instance, the Phelix Day Base Future with maturity 2 refers to a delivery period of all 24 hours of the day starting with the first hour of the day 2 days after the product was traded. This is known as Musiela parameterization (Musiela, 1993) and formally describes a future product f t,m as the price of the future product in t, with the corresponding delivery period starting in t + m. Thus it holds for the time to maturity m that m = min(T) − t. If the delivery period is an interval T = [T 1 , T 2 ], then we have f t,m = F t,T with m = T 1 − t. In the modeling section we consider the Musiela parametrization as well, as was also done for instance in Barndorff-Nielsen et al (2014), Carmona and Coulon (2014) or Benth and Paraschiv (2017).…”