Development of a hybrid model for electrical power spot prices

2005

In recent years a great deal of interest has been paid to the market-based pricing of electrical power. Electrical power contracts often contain embedded options, the valuations of which require a stochastic model for electricity prices. Successful stochastic models exist for modeling price variations in traditional commodities. Electricity is critically different from these commodities as it is difficult to store and, on short time scales, its price is highly inelastic. This has important implications for stochastic spot price models of electricity. Several stochastic models of electricity spot prices already exist. In these random models, price returns play a dominant role.

The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives. This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. Ornstein-Uhlenbeck processes are described as the basic m...

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Energy Economics, 2008

We discuss the modeling of electricity contracts traded in many deregulated power markets. These forward/ futures type contracts deliver (either physically or financially) electricity over a specified time period, and is frequently referred to as swaps since they in effect represent an exchange of fixed for floating electricity price. We propose to use the Heath-Jarrow-Morton approach to model swap prices since the notion of a spot price is not easily defined in these markets. For general stochastic dynamical models, we connect the spot price, the instantaneous-delivery forward price and the swap price, and analyze two different ways to apply the Heath-Jarrow-Morton approach to swap pricing: Either one specifies a dynamics for the non-existing instantaneousdelivery forwards and derives the implied swap dynamics, or one models directly on the swaps. The former is shown to lead to quite complicated stochastic models for the swap price, even when the forward dynamics is simple. The latter has some theoretical problems due to a no-arbitrage condition that has to be satisfied for swaps with overlapping delivery periods. To overcome this problem, a practical modeling approach is analyzed. The market is supposed only to consist of non-overlapping swaps, and these are modelled directly. A thorough empirical study is performed using data collected from Nord Pool. Our investigations demonstrate that it is possible to state reasonable models for the swap price dynamics which is analytically tractable for risk management and option pricing purposes, however, this is an area of further research.

Quantitative Finance, 2004

In this article, we analyze 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, it is demonstrated how it can be used for pricing derivatives via Monte Carlo simulation.

2012

In this paper we propose a new and highly tractable structural approach to spot price modeling and derivative pricing in electricity markets, thus extending the growing branch of literature which describes power price dynamics via its primary supply and demand factors. Using a bid stack approach, our model translates the demand for power and the prices of fuels, used in the power generation process, into spot prices for electricity. We capture both the heavy-tailed nature of spot prices and the complex dependence structure between power and its underlying factors (fuel prices and demand), while retaining simple and commonly used assumptions on the distributions of these factors. Moreover, the derived spot price process then leads to closed form formulae for forward contracts on electricity and for dark and spark spread options, which are widely used for the valuation of power plants. As the stack structure and merit order dynamics are embedded into the model and fuel forward prices ...

Energy Reports, 2019

Pricing option contracts on electricity remains methodologically challenging, with a lack of clearly defined and robust methods. In particular, little is known about pricing options in Brazilian energy markets, despite their economic significance. Using weekly price data (R$/MWh) on four electrical subsystems from the Chamber for Commercialization of Electrical Energy, we estimate models to price Brazilian electricity energy options. This paper has three objectives: (i) to identify the occurrence of change-points (regime-switching) in time series of Brazilian energy spot prices; (ii) to determine the best Stochastic Differential Equation (SDE) with which to model Brazilian energy spot prices and (iii) to price five types of options used to manage electricity price risk in Brazil. We show that the change-point occurred between 2002 and 2018. During this period, the long-run marginal cost of production was the most affected. Furthermore, we find that the Ornstein-Uhlenbeck/Vasicek stochastic process and resulting SDE best explains electricity prices in Brazil, even with the occurrence of structural changes. Finally, our results indicate that Asian-style options are the least costly option contracts to manage electricity price risk in Brazil. Keywords: Energy options Stochastic processes Monte Carlo simulation YUIMA

Econometrics, 2005

In this paper we propose a jump-diffusion type model which recovers the main characteristics of electricity spot price dynamics in the Nordic market, including seasonality, mean-reversion and spiky behavior. We show how the calibration of the market price of risk to actively traded futures contracts allows for efficient valuation of Nord Pool's Asian-style options written on the spot electricity price. Furthermore, we study the evolution of the market price of risk (and the risk premium) over a three year time period and compare the obtained results with those reported in the literature.

2012

The electricity price is a stochastic decision variable which depends on the load, temperature, unit breakdowns, seasonal affects, and workdays etc. Wholesale electricity customers aim to minimize their cost through long term bilateral contracts. One way to deal with the problem is to get electricity options in Turkish derivative markets for future periods which need to be exercised before the expiration date. An option gives the right to consume 0.1 MWH of energy with the strike price for each hour of the month that is the option is exercised. We assume that a wholesale power costumer would like to have options from the market in an effort to get physical energy at the option expiration. The option is exercised only if the strike price is less than the average of the hourly day ahead power prices. This imposes a limit on the strike price that is then used in the Black-Scholes model. Using cyclic behavior of daily power prices and historical price data provided by the market authori...

2010

Electricity markets have several interesting features. For example, electricity spot markets are not free markets, but oligopoly; and due to the low elasticity in the demand, the spot prices have large spikes, which may lead to infinite expectation in the spot prices, although the futures prices have much less spikes and tend to have finite expectations. We propose a two-factor model for on-peak electricity spot and futures prices, starting from the electricity demand. More specifically, we first model the the peak demand as a two-factor mean reverting affine jump diffusion process, attempting to describe two different mean reversion features related to the normal peak demand and abnormal spikes in the demand separately. Then we derive the on-peak spot price based on a minimum Nash equilibrium for the demand-and-price function in oligopoly markets, using the existing game theory results. After constructing a risk-adjusted measure via an equilibrium argument, we obtain analytical solutions for futures prices and call and put options on futures prices. Not only can our model capture some intrinsic features of electricity spot prices, such as mean reversion, spikes, and seasonality, but it is also consistent with the empirical observation that under the physical measure, the on-peak spot prices may have either finite or infinite expectations, while the futures prices tend to have finite means under the physical measure. Numerical examples indicate that our model seems to more reasonable than the existing one-factor models.