Electricity Spot Prices Research Articles

Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach

In this paper we derive analytic formulas for electricity derivatives under assumption that electricity spot prices follow a 3-regime Markov regime-switching model with independent spikes and drops and periodic transition matrix. Since the classical derivatives pricing methodology cannot be used in the case of non-storable commodities, we employ the concept of the risk premium. The obtained theoretical results are then used for the European Energy Exchange data analysis. We calculate the risk premium in the case of the calibrated 3-regime MRS model. We find a time varying structure of the risk premium and an evidence for a negative risk premium (or positive forward premium), especially at short times before delivery. Finally, we use the obtained risk premium to calculate prices of European options written on spot, as well as, forward prices.

An Empirical Comparison of Alternate Schemes for Combining Electricity Spot Price Forecasts

In this paper we investigate the use of forecast averaging for electricity spot prices. While there is an increasing body of literature on the use of forecast combinations, there is only a small number of applications of these techniques in the area of electricity markets. In this comprehensive empirical study we apply seven averaging and one selection scheme and perform a backtesting analysis on day-ahead electricity prices in three major European and US markets. Our findings support the additional benefit of combining forecasts for deriving more accurate predictions, however, the performance is not uniform across the considered markets. Interestingly, equally weighted pooling of forecasts emerges as a viable robust alternative compared with other schemes that rely on estimated combination weights. Overall, we provide empirical evidence that also for the extremely volatile electricity markets, it is beneficial to combine forecasts from various models for the prediction of day-ahead electricity prices. In addition, we empirically demonstrate that not all forecast combination schemes are recommended.

Medium-term planning for thermal electricity production

In the present paper, we present a mid-term planning model for thermal power generation which is based on multistage stochastic optimization and involves stochastic electricity spot prices, a mixture of fuels with stochastic prices, the effect of CO\(_2\) emission prices and various types of further operating costs. Going from data to decisions, the first goal was to estimate simulation models for various commodity prices. We apply Geometric Brownian motions with jumps to model gas, coal, oil and emission allowance spot prices. Electricity spot prices are modeled by a regime switching approach which takes into account seasonal effects and spikes. Given the estimated models, we simulate scenario paths and then use a multiperiod generalization of the Wasserstein distance for constructing the stochastic trees used in the optimization model. Finally, we solve a 1-year planning problem for a fictitious configuration of thermal units, producing against the markets. We use the implemented model to demonstrate the effect of CO\(_2\) prices on cumulated emissions and to apply the indifference pricing principle to simple electricity delivery contracts.

Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes

This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

Changes in electricity spot price formation in Germany caused by a high share of renewable energies

The continuous expansion of electricity generation from intermittent renewable energy sources has already changed the structure of electricity spot prices in Germany considerably. The common method to describe the spot price impacts of renewable energies is to shift the residual load along the merit-order curve of thermal power plants. But, this procedure is undefined if electricity is entirely generated from renewables and conventional power plants are turned off. This paper describes the general feasibility and future challenges to assess the spot price effects of price-elastic demand, substitutive demand and storage during times with surplus of generation from renewable energies.

A methodology for analysis of the renewable electricity feed-in tariff markets

A feed-in tariff model has been enacted in most countries and is well accepted by the European Commission. In principle, the model offers long-term contracts to eligible renewable energy producers, typically based on guaranteed prices for fixed periods of time for electricity produced from renewable energy. This paper presents a methodology that has been developed for the feed-in tariff market approach, which should gradually help eligible producers become better prepared for market competition after long-term contracts expire. The central part of this methodology is the correction of the current guaranteed prices, based on the calculation of the cost-effectiveness ratio of the market model to the current feed-in tariff or non-market model. The common features of the designed market models are the market component, a combination of the guaranteed price with and without market indexing, and the sum of the reduced guaranteed price and the spot electricity price. The methodology has been applied to the current non-market model implemented under Croatian jurisdiction. In this case, seven different market models were designed, which are compared to the existing non-market model. The results of the cost-effectiveness ratio according to different types of renewable energy and market models for a certain period of time are given, described and used for the correction of the current guaranteed price. The first market model has been selected as the most appropriate to replace the existing non-market model in Croatia.

A combined modeling approach for wind power feed-in and electricity spot prices

Abstract Wind power generation and its impacts on electricity prices has strongly increased in the EU. Therefore, appropriate mark-to-market evaluation of new investments in wind power and energy storage plants should consider the fluctuant generation of wind power and uncertain electricity prices, which are affected by wind power feed-in (WPF). To gain the input data for WPF and electricity prices, simulation models, such as econometric models, can serve as a data basis. This paper describes a combined modeling approach for the simulation of WPF series and electricity prices considering the impacts of WPF on prices based on an autoregressive approach. Thereby WPF series are firstly simulated for each hour of the year and integrated in the electricity price model to generate an hourly resolved price series for a year. The model results demonstrate that the WPF model delivers satisfying WPF series and that the extended electricity price model considering WPF leads to a significant improvement of the electricity price simulation compared to a model version without WPF effects. As the simulated series of WPF and electricity prices also contain the correlation between both series, market evaluation of wind power technologies can be accurately done based on these series.

Robust estimation and forecasting of the long-term seasonal component of electricity spot prices

We present the results of an extensive study on estimation and forecasting of the long-term seasonal component (LTSC) of electricity spot prices. We consider a battery of over 300 models, including monthly dummies and models based on Fourier or wavelet decomposition combined with linear or exponential decay. We find that the considered wavelet-based models are significantly better in terms of forecasting spot prices up to a year ahead than the commonly used monthly dummies and sine-based models. This result questions the validity and usefulness of stochastic models of spot electricity prices built on the latter two types of LTSC models.

Identifying spikes and seasonal components in electricity spot price data: A guide to robust modeling

An important issue in fitting stochastic models to electricity spot prices is the estimation of a component to deal with trends and seasonality in the data. Unfortunately, estimation routines for the long-term and short-term seasonal pattern are usually quite sensitive to extreme observations, known as electricity price spikes. Improved robustness of the model can be achieved by (a) filtering the data with some reasonable procedure for outlier detection, and then (b) using estimation and testing procedures on the filtered data. In this paper we examine the effects of different treatments of extreme observations on model estimation and on determining the number of spikes (outliers). In particular we compare results for the estimation of the seasonal and stochastic components of electricity spot prices using either the original or filtered data. We find significant evidence for a superior estimation of both the seasonal short-term and long-term components when the data have been treated carefully for outliers. Overall, our findings point out the substantial impact the treatment of extreme observations may have on these issues and, therefore, also on the pricing of electricity derivatives like futures and option contracts. An added value of our study is the ranking of different filtering techniques used in the energy economics literature, suggesting which methods could be and which should not be used for spike identification.

A jump diffusion model for spot electricity prices and market price of risk

We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for electricity spot prices, while keeping the analytical tractability of futures prices. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices. Moreover, the jump intensity is much higher during summer and winter. We also explore the seasonal market price of risk (MPR) with different maturities, from one month to five months. Our results show that the diffusion risk and the jump risk are priced quite differently.

Retrospective modeling of the merit-order effect on wholesale electricity prices from distributed photovoltaic generation in the Australian National Electricity Market

In electricity markets that use a merit order dispatch system, generation capacity is ranked by the price that it is bid into the market. Demand is then met by dispatching electricity according to this rank, from the lowest to the highest bid. The last capacity dispatched sets the price received by all generation, ensuring the lowest cost provision of electricity. A consequence of this system is that significant deployments of low marginal cost electricity generators, including renewables, can reduce the spot price of electricity. In Australia, this prospect has been recognized in concern expressed by some coal-fired generators that delivering too much renewable generation would reduce wholesale electricity prices. In this analysis we calculate the likely reduction of wholesale prices through this merit order effect on the Australian National Electricity Market. We calculate that for 5GW of capacity, comparable to the present per capita installation of photovoltaics in Germany, the reduction in wholesale prices would have been worth in excess of A$1.8 billion over 2009 and 2010, all other factors being equal. We explore the implications of our findings for feed-in tariff policies, and find that they could deliver savings to consumers, contrary to prevailing criticisms that they are a regressive form of taxation.

Joint Modelling of Gas and Electricity Spot Prices

The recent liberalization of electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this article, we jointly model gas and electricity spot prices using a mean-reverting model that fits the correlation structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions that captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then we simulate some trajectories that reproduce well the observed prices behaviour. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio.

Valuation anomalies for interconnector transmission rights

Whilst the acquisition of physical transmission interconnector rights between two or more electricity markets can be structured as spread options on the spot prices of electricity between connected markets, empirical evidence suggests that actual prices may be quite different. This raises issues for the valuation of transmission rights, particularly in the European context of market harmonisation, and the use of transmission rights with increasing levels of wind penetration. We examine the price differentials between the Irish and British electricity markets, where explicit transmission capacity auctions have been persistently undersubscribed and transmission rights acquired but not fully utilised. We find significant empirical indications that auction prices for transmission rights are undervalued against both arbitrage and spread option valuations. We also find significant power flows against the efficient price spread direction. A survey of a group of experts with an interest in trading power between Ireland and Britain inform a number of possible explanations for the apparent inefficiencies. These include ex-post pricing in the Irish market, intermittent wind and strategic behaviour by dominant firms.

Modelling Higher Moments of Electricity Prices

It is crucial to model, quantify and understand the variables and dynamics that underlie the well-known extreme behaviour of spot electricity prices in wholesale markets. We explicitly model the conditional volatility and skewness of electricity prices. A GARCH-type model allowing for time-varying volatility and skewness, which is estimated assuming a Gram-Charlier expansion of the normal density function, is presented. This model is applied to data from Pennsylvania- New Jersey, NordPool and Victoria (Australia) markets. We document the existence of a rich structure in the conditional skewness of spot prices and we show the relationship between skewness and demand-supply related variables.

Forecasting Electricity Spot Prices Accounting for Wind Power Predictions

A two-step methodology for forecasting of electricity spot prices is introduced, with focus on the impact of predicted system load and wind power generation. The nonlinear and nonstationary influence of these explanatory variables is accommodated in a first step based on a nonparametric and time-varying regression model. In a second step, time-series models, i.e., ARMA and Holt-Winters, are applied to account for residual autocorrelation and seasonal dynamics. Empirical results are presented for out-of-sample forecasts of day-ahead prices in the Western Danish price area of Nord Pool's Elspot, during a two year period covering 2010-2011. These results clearly demonstrate the practical benefits of accounting for the complex influence of these explanatory variables.

Diffusion of PV in Japan and Germany-Role of Market-Based Incentive and Research and Development (R&D) Investment

The goals of increasing the use of PV energy face significant obstacles. Regulatory requirements can be used to mandate the adoption of renewable energy, but market-based incentive mechanisms can also achieve the same results by inducing voluntary behavior from stakeholders. Variations in terms of both design and implementation of market-based incentives can have meaningful effects on the outcomes of incentive programs. We examine Japan and Germany in which PV energy accounts for a relatively high portion of total net electricity energy consumption. Germany FITs were originally linked to the spot electricity price, but a fixed tariff was adopted in 2000, and revised in 2004. A grant program also funds a portion of construction costs for new PV systems. The country has experienced rapid uptake of renewables over the past decade, making it a world leader in solar PV at the end of 2008. The purpose of this study is to analyze the PV diffusion in Japan and Germany during 1990-2011. Germany chooses an effective market-based incentive mechanism which is long term and more generous than Japanese incentive program. The termination of incentive policy is the main blocking factor of the decline of PV market in Japan.

Diffusion of PV in Japan and Germany-Role of Market-Based Incentive and Research and Development (R&D) Investment

The goals of increasing the use of PV energy face significant obstacles. Regulatory requirements can be used to mandate the adoption of renewable energy, but market-based incentive mechanisms can also achieve the same results by inducing voluntary behavior from stakeholders. Variations in terms of both design and implementation of market-based incentives can have meaningful effects on the outcomes of incentive programs. We examine Japan and Germany in which PV energy accounts for a relatively high portion of total net electricity energy consumption. Germany FITs were originally linked to the spot electricity price, but a fixed tariff was adopted in 2000, and revised in 2004. A grant program also funds a portion of construction costs for new PV systems. The country has experienced rapid uptake of renewables over the past decade, making it a world leader in solar PV at the end of 2008. The purpose of this study is to analyze the PV diffusion in Japan and Germany during 1990-2011. Germany chooses an effective market-based incentive mechanism which is long term and more generous than Japanese incentive program. The termination of incentive policy is the main blocking factor of the decline of PV market in Japan.

Electricity price modeling and asset valuation: a multi-fuel structural approach

We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity spot prices. The stack structure allows for a range of generator efficiencies per fuel type and for the possibility of future changes in the merit order of the fuels. The derived spot price process captures important stylized facts of historical electricity prices, including both spikes and the complex dependence upon its underlying supply and demand drivers. Furthermore, under mild and commonly used assumptions on the distributions of the input factors, we obtain closed-form formulae for electricity forward contracts and for spark and dark spread options. As merit order dynamics and fuel forward prices are embedded into the model, we capture a much richer and more realistic dependence structure than can be achieved by classical reduced-form models. We illustrate these advantages by comparing with Margrabe's formula and a simple cointegration model, and highlight important implications for the valuation of power plants.

Fitting semiparametric Markov regime-switching models to electricity spot prices

Recently regime-switching models have become the standard tool for modeling electricity prices. These models capture the main properties of electricity spot prices well but estimation of the model parameters requires computer intensive methods. Moreover, the distribution of the price spikes must be fully specified although the high volatility of the spikes makes it difficult to check such distributional assumptions. Consequently, there are a number of competing proposals for the distribution in the spike regime. As an alternative, we propose a semiparametric Markov regime-switching model that leaves the distribution under the spike regime unspecified. We show that the model parameters can be estimated by employing robust statistical techniques. This presents an alternative to the existing estimation methods that are based on computer intensive numerical maximization of the likelihood function. The model in combination with the estimation framework is easier to estimate, needs less computation time and distributional assumptions. To show its advantages we compare the proposed model with a well-established Markov regime-switching model in a simulation study. Furthermore, we apply the model to log-prices for the Australian electricity market. The results are in accordance with the results from the simulation study, indicating that the proposed model might be advantageous whenever the distribution of the spike process is not sufficiently known. The results are thus encouraging and suggest the use of our approach when modeling electricity prices and pricing derivatives.

A Probabilistic Numerical Method for Optimal Multiple Switching Problems in High Dimension

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors.