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ELECTRICITY SPOT PRICES ANALYZED: A REGIME-SWITCHING APPROACH.
M. Kilic, Erasmus School of Economics, Erasmus University Rotterdam, +31 10 408 8932, kilic@ese.eur.nl
R. Huisman, Erasmus School of Economics, Erasmus University Rotterdam, +31 10 408 8925, rhuisman@ese.eur.nl
Overview
The primary goal of the liberalization process has been to create a single European power market by introducing competition in the electricity market. A competitive market should result in a convergence towards an equilibrium single price, however the electricity prices in the liberalized power markets fluctuate heavily. The most evident features of electricity price dynamics are the presence of seasonality, mean-reversion, time-varying volatility and price spikes. In this paper, we question to what extent the typical features of electricity spot prices in different deregulated markets developed over the years. To do so, we examine day-ahead electricity prices for the Belgian, Dutch, German, French and Scandinavian markets over the years 2003 until 2010. The stylized facts of the electricity spot prices can be captured by the Markov regime-switching model. Overall we see that over the years the prices are more stabilized and the markets behave more alike except for the Scandinavian market, which shows an opposite pattern.
Methods
Regime-switching models offer the possibility to introduce various mean reversion rates and volatilities depending on the state of the system. This approach is flexible enough to be used in modelling electricity prices dynamics in order to distinguish the normal stable motion from the turbulent spike regime. The regime-switching model is used for modelling price spikes and is derived by gradually extending the basic mean-reverting specification to include spikes (Lucia and Schwartz, 2001). Let S(t) be the natural logarithm of the day-ahead price for delivery of 1 MW on day t. The spot price is assumed to be the sum of a deterministic component d(t) and a stochastic component x(t).
d(t) is a highly predictable component accounting for the seasonality effects and x(t) is the random component reflecting unpredictable movements of the prices (Hamilton, 1994). The construction of the model is based on Mount et. al. (2006) and Huisman (2008).
(1)
The deterministic component consists of a mean price level 1 and allows for a different price for weekend delivery reflected by (. The parameter ( is expected to be negative as weekend days normally exhibit lower prices than working days. w(t) is the weekend dummy variable which incorporates seasonality in the estimation process and is 1 if t is a weekend day and 0 if it is any other day.
(2)
The stochastic component in the normal regime consists of a mean reversion component with speed of mean reversion ( and a normally distributed error term T1,t. with standard deviation 1.
(3)
The stochastic component in the abnormal regime consists of a mean price 2, which is the increase in the price level in the abnormal regime. T2,t is a normally distributed error term with standard deviation 2.
(4)
The transition probability is determined by a random variable that follows a Markov chain with different possible states. The transition probability for switching from one regime to the other regime as logistic functions ensures that predicted probabilities are between 0 and 1. The element Pi,t denotes the conditional probability that the process is in regime i at time t given that the process was in regime i at time t"1: Pi,t = Pr St=i|St"1 = i.
The transition probability 1-Pi,t equals the probability from being in regime i at time t"1 and moving to the other regime in the next day. The transition probabilities are assumed to be constant over time:
(5)
The transition probabilities for switching from one regime to the other regime as logistic functions ensures that predicted probabilities are between 0 and 1. The actual value of the probability, is determined with:
(6)
Results
Focusing firstly on the different parameters of the regime-switching model for the APX, BELPEX, EEX and EPEX market we observe that the different parameters develop comparably. 1, which is the mean log price level in the normal regime, is increasing and the increase in the price level in the abnormal regime (2) is declining for all four markets. This designates the lower price movements in the abnormal regime over time. The occurrence of a negative 2 indicates that the price spike characteristic in the electricity market has changed over the years. We observe that 1-p11, which shows the probability of a price spike, decreases for the APX, BELPEX and EPEX markets and increases for the EEX and NPX markets. Therefore price spikes did not disappear, however the size of the spikes became smaller and therefore are not identified as a spike by the market. (, which is the speed of mean reversion under normal market conditions, shows a significant decline for all four markets. Meaning that it will take longer to return to the mean price level after a fluctuation. Studying the volatility of the prices in the normal and abnormal regime we see a decline in the values of 1 and 2. This indicates a decrease in the volatility of the prices in both regimes. Low volatility in the abnormal regime (2) implies that the level of expected price spikes is quite predictable, since the variation is small and will remain close to the mean spike size. Therefore the spikes are becoming less variable over time and result in lower price movements. The low volatility in the abnormal regime combined with the low price spike mean indicates that the day-ahead prices in the APX, BELPEX, EEX and EPEX markets are more stable seeing that the difference between the normal and abnormal regime declines. This also suggests more liquidity in the day-ahead markets. The weekend factor (, which is the difference in mean price level between weekend and workdays shows a significant rise from -0.5 for the APX, BELPEX and EEX market to -0.4 and for the EPEX market to -0.2, implying that the difference between weekend and workdays mean log price is smaller and thus less weekend seasonality. The Scandinavian market (NPX) shows a total different pattern with increasing parameters. Unlike for the APX, BELPEX, EEX and EPEX markets (, 2 and 1 are increasing. In the normal regime there is more price fluctuation, however after a fluctuation the prices revert faster to the mean price level.
Secondly we observe that the parameter estimations are converging through time. First of all the Dutch electricity market is connected with the Belgian, German and Scandinavian markets and is indirectly influenced by the French market through its interconnection with Belgium. The NPX market does not show any sign of convergence with APX. In 2010 we observe that for APX, BELPEX, EEX and EPEX the mean log price level in the normal regime (1) converges to 3.9 and does not significantly differ between these markets. 2 converges to -0.2, however for the APX market 2 is -0.1. The increase of the mean log price level in the abnormal regime (2) shows a decrease in the significance level and in the year 2010 this difference is not significant anymore. The weekend seasonality ( converges significantly to -0.2. The speed of mean reversion ( converges significantly to 0.2, except for EEX ( is 0.3 and the difference is significant. The volatility of the prices in the normal regime converges to 0.1 and for the abnormal regime to 0.2, however not significant. Secondly the Belgian market is also connected with the French electricity market. All parameter estimations show convergence and the decline of the t-statistic indicate that there is no significant difference between these parameters.
Conclusions
This paper questions to what extent the typical features of electricity spot prices in different deregulated markets developed over the years. We find a significant change in the electricity spot prices of the Netherlands (APX), Belgium (BELPEX), Germany (EEX), France (EPEX), and the Scandinavian market (NPX). The electricity spot prices show an increase in price correlations and this will cause a higher level of market integration between these power exchanges. Overall we see that over the years the prices are more stabilized and that the markets are behaving more alike except for the Scandinavian market, which shows an opposite pattern.
References
J.D. Hamilton. Time Series Analysis. Princeton University Press, 1994.
R. Huisman. The influence of temperature on spike probability in day-ahead power prices. Energy Economics, 30:26972704, 2008.
J. Lucia and E. Schwartz. Electricity prices and power derivatives: evidence from the Nordic power exchange. Review of Derivatives Research, 5:550, 2002.
T.D. Mount, Y. Ning, X. Cai. Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Economics, 28:6280, 2006.
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