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A regime-switching model for electricity spot prices
Abstract
Electricity markets exhibit a number of typical features that are not found in most financial markets, such as price spikes and complex seasonality patterns. This paper proposes a sto-chastic model for electricity spot prices that is based on a regime-switching approach applied to average daily prices . Two different regimes represent a "normal" and a "spike" regime, the latter characterized by high volatility and strong mean-reversion. The model is calibrated via a maximum-likelihood optimization in connection with a Hamilton filter for the unobservable regime-switching process. Given the daily prices, the hourly price profiles are modelled us-ing a principal component analysis for the 24-hour price vectors and afterwards setting up a time-series model for the factor loads. Example results are shown for spot price data from the European Energy Exchange EEX.
... A regime-switching model is used by Schindlmayr to predict spot price data from the European Energy Exchange (Schindlmayr, 2005). The author uses two regimes, one to represent a normal regime, and another for a spike regime, where the spikes are character- Another piece of data that we use in the prediction of the price time series is hourly data on wind power generation, published real-time on the ERCOT website, and made available for research purposes. ...
... [50] and [5] use regimeswitching processes to model term structures of interest rates. Various regime-switching models are calibrated to electricity spot prices in [37,55,36,35,77]. ...
... A similar analysis for electricity, gas and oil prices is given by Huisman & Mahieu (2003). Schindlmayr (2005) models the EEX prices with a regime-switching model where spot prices switch between two regimes. They follow a mean reversion process in both regimes but have a regime-dependent mean reversion rate and volatility. ...
... Electricity markets exhibit a number of typical features that are also found in the financial markets to some degree, such as price spikes and complex seasonality patterns. Spot prices may even show extreme price spikes that are the result of unplanned outages or capacity limits of generation or transmission assets or a sudden, unexpected and substantial change in demand [25,26]. Market mechanism failure and capacity constraints in the network may cause spikes, because they lead to temporary deviations from efficient competition in the market [27]. ...
The European Energy Exchange (EEX) day ahead spot market for electricity in Germany shows significant variations in prices between peak and off-peak hours. Being able to shift electricity production from off-peak hours to peak hours improves the profit from CHP-plant operation significantly. Installing a big thermal store at a CHP-plant makes it possible to shift production of electricity and heat to hours where electricity prices are highest especially on days with low heat demand. Consequently, these conditions will have to influence the design of new CHP-plants. In this paper, the optimal size of a CHP-plant with thermal store under German spot market conditions is analyzed. As an example the possibility to install small size CHP-plant instead of only boilers at a Stadtwerke delivering 30,000 MW h-heat for district heating per year is examined using the software energyPRO. It is shown that, given the economic and technical assumptions made, a CHP-plant of 4 MW-el with a thermal store participating in the spot market will be the most feasible plant to build. A sensitivity analysis shows to which extent the optimal solution will vary by changing the key economic assumptions.
There has been an increasing interest on pricing power plants. The main reasons are making power investment decisions, related to the risks derived from managing or investing in combined cycle power plants. A stochastic model for the electricity futures curve has been applied for studying, using the option pricing theory framework, the pricing and hedging of a combined cycle power plant. The solution is obtained by means of solving a stochastic control problem over any feasible future load strategy. We discuss the practical case of hedging against market futures the plant risks. Finally we test against market historical values, the validity of the hedging strategy.
The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, namely power, oil, gas, coal and carbon.The objective of the paper is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants which represent typical energy portfolios.Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plant.
In the last decades a liberalization of the electric market has started; prices are now determined on the basis of contracts on regular markets and their behaviour is mainly driven by usual supply and demand forces. A large body of literature has been developed in order to analyze and forecast their evolution: it includes works with different aims and methodologies depending on the temporal horizon being studied. In this survey we depict the actual state of the art focusing only on the recent papers oriented to the determination of trends in electricity spot prices and to the forecast of these prices in the short run. Structural methods of analysis, which result appropriate for the determination of forward and future values are left behind. Studies have been divided into three broad classes: Autoregressive models, Regime switching models, Volatility models. Six fundamental points arise: the peculiarities of electricity market, the complex statistical properties of prices, the lack of economic foundations of statistical models used for price analysis, the primacy of uniequational approaches, the crucial role played by demand and supply in prices determination, the lack of clearcut evidence in favour of a specific framework of analysis. To take into account the previous stylized issues, we propose the adoption of a methodological framework not yet used to model and forecast electricity prices: a time varying parameters Dynamic Factor Model (DFM). Such an eclectic approach, introduced in the late '70s for macroeconomic analysis, enables the identification of the unobservable dynamics of demand and supply driving electricity prices, the coexistence of short term and long term determinants, the creation of forecasts on future trends. Moreover, we have the possibility of simulating the impact that mismatches between demand and supply have over the price variable. This way it is possible to evaluate whether congestions in the network (eventually leading black out phenomena) trigger price reactions that can be considered as warning mechanisms.
In this paper, we propose a one-factor regime-switching model for the risk adjusted natural gas spot price and study the implications of the model on the valuation and optimal operation of natural gas storage facilities. We calibrate the model parameters to both market futures and options on futures. Calibration results indicate that the regime-switching model is a better fit to market data compared to a one-factor mean-reverting model similar to those used by other authors to value gas storage. We extend a semi-Lagrangian timestepping scheme from Chen and Forsyth (200713.
Chen , Z and
Forsyth , PA . 2007. A semi-Lagrangian approach for natural gas storage valuation and optimal operation. SIAM J. Sci. Comput., 30: 339–368. [CrossRef], [Web of Science ®]View all references) to solve the gas storage pricing problem, essentially a stochastic control problem, and conduct a convergence analysis of the scheme. Numerical results also indicate that the regime-switching model can generate operational strategies for gas storage facilities that reflect the existence of multiple regimes in the market as well as the regime shifts due to various exogenous events.
The wavelet transform is used to identify a biannual and an annual seasonality in the Phelix Day Peak and to separate the long-term trend from its short-term motion. The short-term/long-term model for commodity prices of Schwartz & Smith (2000) is applied but generalised to account for weekly periodicities and time-varying volatility. Eventually we find a bivariate SARMA-CCC-GARCH model to fit best. Moreover it surpasses the goodness of fit of an univariate GARCH model, which shows that the additional effort of dealing with a two-factor model is worthwile. --
In the last decades a liberalization of the electric market has started; prices are now determined on the basis of contracts on regular markets and their behaviour is mainly driven by usual supply and demand forces. A large body of literature has been developed in order to analyze and forecast their evolution: it includes works with different aims and methodologies depending on the temporal horizon being studied. In this survey we depict the actual state of the art focusing only on the recent papers oriented to the determination of trends in electricity spot prices and to the forecast of these prices in the short run. Structural methods of analysis, which result appropriate for the determination of forward and future values are left behind. Studies have been divided into three broad classes: Autoregressive models, Regime switching models, Volatility models. Six fundamental points arise: the peculiarities of electricity market, the complex statistical properties of prices, the lack of economic foundations of statistical models used for price analysis, the primacy of uniequational approaches, the crucial role played by demand and supply in prices determination, the lack of clearcut evidence in favour of a specific framework of analysis. To take into account the previous stylized issues, we propose the adoption of a methodological framework not yet used to model and forecast electricity prices: a time varying parameters Dynamic Factor Model (DFM). Such an eclectic approach, introduced in the late ‘70s for macroeconomic analysis, enables the identification of the unobservable dynamics of demand and supply driving electricity prices, the coexistence of short term and long term determinants, the creation of forecasts on future trends. Moreover, we have the possibility of simulating the impact that mismatches between demand and supply have over the price variable. This way it is possible to evaluate whether congestions in the network (eventually leading black out phenomena) trigger price reactions that can be considered as warning mechanisms.
Objective of this paper is to gain insights into jump occurrences and to enhance the understanding of modelling jumps in electricity markets. We provide a common modelling framework that allows to incorporate the main jump patterns observed in electricity spot prices and compare the effectiveness of different jump specifications. To this end, we calibrate the models to daily EEX market data through Markov Chain Monte Carlo based methods. To assess the quality of the estimated jump processes, we analyse their trajectorial and statistical properties and compare them to market data. Moreover, we discuss the associated model risk when calibrating the models to the forward curve and using the approaches for derivatives pricing.
The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return distribution of energy related commodities futures, namely power, oil, gas, coal and carbon. The objective of the paper is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the epxosure of power plants which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plant.
In this paper, we analyse the evolution of prices in deregulated electricity markets. We present a general model that simultaneously takes into account the following features: seasonal patterns, price spikes, mean reversion, price dependent volatilities and long term non-stationarity. We estimate the parameters of the model using historical data from the European Energy Exchange. Finally, we demonstrate how it can be used for pricing derivatives via Monte Carlo simulation.
We address the issue of modeling spot electricity prices with regime switching models. After reviewing the stylized facts about power markets we propose and fit various models to spot prices from the Nordic power exchange. Afterwards we assess their performance by comparing simulated and market prices. 1 Electricity Spot Prices: Markets and Models The deregulation of the power industry has given way to a global trend toward the commoditization of electric energy. Electricity has transformed from a primarily technical business, to one in which the product is treated in much the same way as any other commodity, with trading and risk management as key tools to run a successful business [2,12,15]. However, we have to bear in mind that electricity is a very unique commodity. It cannot be economically stored, demand of end users is largely weather dependent, and the reliability of the transmission grid is far from being perfect. This calls for adequate models of price dynamics capturing the main characteristics of spot electricity prices.
Electricity prices are known to be very volatile and subject to frequent jumps due to system breakdown, demand shocks, and inelastic supply. Appropriate pricing, portfolio, and risk management models should incorporate these spikes. We develop a framework to price European-style options that are consistent with the possibility of market spikes. The pricing framework is based on a regime jump model that disentangles mean-reversion from the spikes. In the model the spikes are truly time-specific events and therefore independent from the mean-reverting price process. This closely resembles the characteristics of electricity prices, as we show with Dutch APX spot price data in the period January 2001 till June 2002. Thanks to the independence of the two price processes in the model, we break derivative prices down in a mean-reverting value and a spike value. We use this result to show how the model can be made consistent with forward prices in the market and present closed-form formulas for European-style options.
This paper presents a family of processes to model electricity spot prices in deregulated markets. Besides mean-reversion, a property they share with other comodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a « jump-reversion » component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture – for the first time to our knowledge – both the trajectorial and statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major US power markets.
I propose several mean-reversion jump-diffusion models to describe spot prices of energy commodities that maybevery costly to store. I incorporate multiple jumps, regime-switching and stochastic volatility into these models in order to capture the salient features of energy commodity prices due to physical characteristics of energy commodities. Prices of various energy commodity derivatives are derived under each model using the Fourier transform methods. In the context of deregulated electric power industry, I construct a real options approachtovalue physical assets such as generation and transmission facilities. The implications of modeling assumptions to the valuation of real assets are also examined.
StochasticModelsofEnergyCommodityPricesandTheirApplications: Mean-reversion with Jumps and Spikes, Working paper
- S Deng
S.Deng, StochasticModelsofEnergyCommodityPricesandTheirApplications: Mean-reversion with Jumps and Spikes, Working paper, Georgia Institute of Technology, 2000.
Weron Modelling electricity prices with regime switching models Lecture Notes in Computer Sciences
- M Bierbrauer
- S Trück
M. Bierbrauer, S. Trück, and R. Weron Modelling electricity prices with regime switching models Lecture Notes in Computer Sciences, 07/2004