Fred Espen Benth
University of Oslo
This special issue contains five papers that were presented at the “Conference on Energy Finance” (Kristiansand, Norway, September 24–25, 2009). The conference focused on recent trends in the modeling and management of risk in energy markets, and attracted participants from both academia and industry. The complexity of energy markets calls for sophisticated stochastic models to capture the dynamics of prices. Energy derivatives often have exotic optionality involving not only several exercise times but, in many cases, volume control as well. The analysis of these derivatives is based on stochastic control theory. Both the calibration of energy price models and the analysis of derivatives require advanced computerintensive simulation methods. The characteristic feature of all the contributed papers in this special issue is the important role that efficient computational methods play. One may predict that this trend will also play a major role in energy finance in the near future.
There is empirical evidence in the forward markets of leptokurtic returns and a significant amount of idiosyncratic risk, both of which call for random field models. In the first paper in the issue, “Modeling electricity forward prices using the multivariate normal inverse Gaussian distribution”, Andresen, Koekebakker and Westgaard propose modeling forward price returns using a multivariate normal inverse Gaussian distribution, where the correlation between contracts is modeled as a parametric function of time to maturity and includes seasonality. The model is calibrated to data in the Nord Pool market using a Markov chain Monte Carlo method. The model fits many of the stylized facts of electricity forward return data, and is, at the same time, analytically tractable for option pricing.
In the second paper, “The valuation of power futures based on optimal dispatch”, De Maere D’Aertrycke and Smeers are also concerned with the forward market for electricity. In their paper, an equilibrium model for the valuation of power futures is developed, taking into account the main fundamental factors for electricity generation; demand, fuel and carbon prices. The futures prices can be computed as the solution of a higher-dimensional partial differential equation, extending the Pirrong–Jermakyan framework. From a numerical study of the German European Energy Exchange (EEX) market, the authors find that there is a significant market price of risk for peakload contracts, but almost no risk pricing in baseload contracts.
In the third paper, “Pricing electricity derivatives on an hourly basis”, Branger, Reichmann and Wobben analyze power derivatives in a two-factor model for the electricity spot price. The spot price dynamics incorporates seasonality, jumps and mean reversion, and allows for analytic forward pricing. The authors estimate the risk premium in the EEX market based on the estimated spot model. Options like calls on electricity forwards, physical transmission rights and a class of spread options are investigated, and theoretical prices are compared with market quotations. Based on their findings, the authors argue that there is mispricing of these derivatives in the markets.
Swing options are another interesting class of derivatives in the energy market. In the fourth paper, “Valuation of commodity-based swing options”, Kiesel, Gernhard and Stoll develop a least-squares Monte Carlo algorithm to price such derivatives. Their method is an extension of the Longstaff–Schwartz algorithm for valuation of American options using regression to approximate conditional expectations. A class of swing options commonly used in the oil market, where there is a recovery time between the swings, is the subject of a concrete numerical study. The price and optimal exercise strategy are found, and they are compared with the results from a numerical method based on the solution of a variational inequality.
In the fifth paper, “A spot price model for natural gas considering temperature as an exogenous factor with applications”, Stoll andWiebauer propose a model for the gas spot price with an index of temperature as an exogenous variable. An empirical analysis of daily day-ahead and weekend Title Transfer Facility gas prices from the Netherlands demonstrates that the heating degree days index has a strong influence on gas spot price dynamics. The authors propose and estimate models for gas spot prices and temperatures based on autoregressive moving average processes. The model is applied to the valuation of gas storage and the pricing of full supply contracts for customers whose consumption depends strongly on temperature. The valuations are based on a least-squares Monte Carlo approach.
The conference in Kristiansand is the fifth in a series of annual meetings on energy finance, attracting participants from both academia and industry. Previous conferences have been held in Ulm, London, Oslo and Karlsruhe. This autumn the event takes place in Essen, the cultural capital of Europe. The best papers will again appear in a special issue of the Journal of Energy Markets.