Pricing Electricity Forwards using the Real Option Theory

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.

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

This Ph. D. dissertation deals with the pricing of derivatives on electricity price. It belongs to the field of Arbitrage Pricing Theory and financial mathematics. The first part is a theoretical extension of Arbitrage Pricing Theory: we assess the problem of pricing European contingent claims when the financial agent has the possibility to transform assets by means of production possibilities. We propose a specific concept of arbitrage for such portfolios and extend some results of Rásonyi [Rásonyi 10] in discrete time for markets ...

Energy Economics, 2019

In liberalized electricity markets, ongoing uncertainties play a major role to delay the decision-making of new power generation investments.  A valuation framework of power plant investments, based on Real Options Analysis, is integrated with a long-term electricity market model.  The decision-making model considers that the addition of new power capacity is guided by the economic value of the option to defer projects under uncertainty.  The main contribution is the integration of decision and option valuation theory in a long-term model for reproducing investment cycles observed in electricity markets.

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.

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.

Power Systems, IEEE …, 2002

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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...

Energija, 2007

Rizik od stalnih promjena cijena moguÊe je umanjiti koriπtenjem razliËitih fi nancijskih instrumenata. U tu skupinu instrumenata spadaju ugovori o opcijama, odnosno opcije. Po njima kupac otkupljuje pravo na ugovorene cijene nekog predmetnog sredstva, na primjer elektriËne energije. S obzirom na varljivost cijena kupac ne mora izvesti opciju. Tada je njegov jedini gubitak otkupljeno pravo ili premija, πto odgovara vrijednosti jedne opcije. MatematiËki modeli za odreivanje vrijednosti opcija razvijaju se veÊ viπe od sto godina. No, svoj procvat doaeivljaju sedamdestih godina 20. stoljeÊa zahvaljujuÊi formuli Black-Scholes kojom se odreuje teoretska vrijednost opcija. U Ëlanku se daje podjela opcija po razliËitim kriterijima, opisuju naËini njihovog izvoenja te prati povijesni razvoj modela za odreivanje vrijednosti opcija. Izloaeen je primjer izvoenja opcije na najveÊoj srednjoeuropskoj burzi elektriËne energije EEX uz primjenu margina. Continual price fl uctuations are possible to hedge by using various fi nancial instruments, including options. An option buyer buys the right to the settlement price of an underlying asset such as electricity. Due to the volatility of the asset price, the buyer is not obliged to exercise the option. In such a case, the buyer's only loss is the purchased right or the option premium, which is equal to the option price. Mathematical models for option pricing have been developed in the last hundred years. These models were very popular during the 1970s, owing to the application of the Black-Scholes formula for the calculation of theoretical option prices. In this article, options are distinguished according to various criteria, specifi c exercising methods are described and the historical development of option pricing models is reviewed. An example of option exercising with closing out of the margins on the largest Middle European electricity exchange, EEX, is presented.

2015

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...