A spot-forward model for electricity prices with regime shifts

Florentina Paraschiv, Stein-Erik Fleten, Michael Schürle
2015 Energy Economics  
We propose a novel regime-switching approach for electricity prices in which simulated and forecasted prices are consistent with currently observed forward prices. Additionally, the model is able to reproduce spikes and negative prices. We distinguish between a base regime as well as upper and lower spike regimes. We derive hourly price forward curves for EEX Phelix, and together with historical hourly spot prices, historical hourly price forward curves are the basis for model calibration. The
more » ... odel can be used for simulation and forecasting of electricity spot prices over short-and medium-term horizons. Tests imply that it shows a better performance than classical time series approaches. and reduce price predictability. Finding realistic models to describe electric-8 ity prices is essential for the valuation of power contracts, for risk managers 9 for the estimation of risk measures as well as for portfolio managers for the 10 identification of worst-case scenarios in very turbulent markets. 11 Dependent on the research question and planning task different models 12 for electricity prices are proposed in the literature. Fundamental models 13 take into account the components of the whole electricity system and serve 14 for long-term planning (see [14] ). Game theoretic approaches analyse the 15 strategic behavior of different market participants ([11, 17]) and account 16 for market design options. Financial mathematical models deal with the 17 volatility of electricity prices and are often used for the evaluation of energy 18 derivatives ([22]). Econometric time-series models like ARMA and GARCH 19 processes are applied to simulate and forecast electricity prices for a short-20 term planning period and reflect specific patterns such as autocorrelation 21 (see [7, 18, 27]). 22 The models discussed earlier describe in general typical characteristics of 23 electricity prices like seasonality patterns, mean reversion or volatility clus-24 tering. However, beside these aspects, an important characteristic to be 25 considered is the extreme price changes that are reflected by the so-called 26 "spiking" behavior of power prices. These spikes occur mainly because elec-27 tricity is non-storable which causes demand and supply to be balanced on 28 a "knife-edge" (see [25]). Relatively small changes in the load or genera-29 tion can cause extreme price changes between consecutive hours. The spik-30 ing behavior is often described in the literature by regime-switching models 31 ([2, 12, 13, 25, 26, 27]). The authors conclude in general that regime switch-32 ing models lead to a better modeling performance than the other models 33 mentioned before. They additionally allow electricity prices to switch be-34 tween a "base" regime and a "jump" regime. Jumps are modeled by a jump 35 diffusion process, or the regimes are governed by an unobservable, stochastic 36 process (Markov regime-switching models). 37 We propose a novel regime-switching approach for electricity prices in 38 which simulated and forecasted spot prices are consistent with currently ob-39 served forward prices. Every day, futures prices are observed in the market 40 and an hourly price forward curve (HPFC) is derived. The typical seasonality 41 pattern of electricity prices is additionally used to model the curve. The for-42 ward price of a particular day and hour provides information on the expected 43 spot price of that day/hour. This is used to generate simulations or forecasts 44 of future spot prices. Since the HPFC extends to the longest available ma-45 48 and allows for spike clustering and for negative prices. This is important 49 since prices jump into another spike regime and can remain there for some 50 hours (see the discussion in [12] or [13]). Furthermore, negative prices occur 51 at EEX since 1 September 2008 due to the special characteristics of electricity 52 markets, e.g., limited storage capacities, limited load change flexibility and 53 combined production of heat and power. 54 Most spot price simulation models cited earlier lack consistency with the 55 market because the information about the expected future spot prices re-56 flected in the forward curve is not taken into account. For risk management 57 applications in particular, such as hedging of price risk or valuation of power 58 contracts, consistency with the observed forward prices is essential. This 59 means that forecasted and simulated spot prices are adjusted for risk, allow-60 ing for straightforward valuation procedures. Compared to classical time-61 series models, our regime-switching model also leads to a significantly better 62 in-and out-of-sample fit and can be used for long-term simulations of spot 63 prices with the current HPFC as input. 64 The idea of using information from the HPFC in a regime-switching model 65 was also used in [16] in the context of scenario generation within a stochastic 66 optimization model for medium-term power production planning. However, 67 there deviations from the forward curve and spikes were modeled as indepen-68 dent events. We extend this approach by introducing also serial dependencies 69 and a transition probability matrix to model spike clusters. Additionally, the 70 variation of spot prices and spikes may now be season-dependent. For the 71 generation of the input HPFC we use here a more suitable methodology to 72 reflect the intra-day seasonality pattern. 73 This paper is organized as follows: In Section 2 we summarize charac-74 teristics of electricity spot prices and consequences for the model structure. 75 Based on these considerations, Section 3 outlines the derivation of HPFCs 76 and introduces the formal specification of the regime switching model. The 77 corresponding estimation procedure is described in Section 4 and the ob-78 tained results are discussed in Section 5. In Section 6 we show the compar-79 ative performance of the regime-switching model versus classical time-series 80 models and results of simulation runs. Section 7 discusses the use of the 81 model for short-and medium-term forecasts. Finally, Section 8 concludes. 82
doi:10.1016/j.eneco.2014.11.003 fatcat:lgc3l35blfdizidpsiaqg4rduy