Energy markets continue to offer great potential for the application of advanced modeling techniques. Price formation (whether for power, gas or oil) is complex in nature, and the stochastic and extreme value properties of those prices and their interrelationships form important risk-related topics for which innovative methods of analysis can provide real practical value. The Journal of Energy Markets works at the forefront of this research and this issue is an excellent representation.
In the issue's first paper, "Computation of Greeks in multifactor models with applications to power and commodity markets" by Fred Espen Benth, Giulia Di Nunno and Asma Khedher, a new approach is applied to the computation of option parameters, where the underlying assets are modeled using multifactor dynamics. The novel aspect is the application of a conditional density method, for which knowledge of the density of one factor is sufficient to derive expressions for the Greeks without involving any differentiation of the payoff function. Several numerical examples are
given for applications to power and other markets.
On a related theme, the second paper in the issue, "Estimating a Lévy multifactor market model for electricity futures markets by using independent component analysis" by Giuseppe Di Poto and Enzo Fanone, looks specifically at electricity futures and forward contracts. The dynamics of these derivatives is also modeled as a multifactor market model, where the idea is to match the observed volatility term structure and correlation surface among different electricity futures deliveries. The authors propose a Lévy multifactor model for electricity futures contracts with nonoverlapping delivery periods, in the particular case of the normal inverse Gaussian, in order to capture the heavy tails that are not described by the normal distribution. The paper uses the independent component analysis method, which can handle leptokurtic data, in order to decompose the correlation/covariance matrix. Numerical examples using power data from the European energy exchange and Powernext show the value of this new approach.
An explicit focus on the tails is pursued further in the issue's third paper: "Modeling dependence of extreme events in energy markets using tail copulas" by Stefan Jäschke, Karl Friedrich Siburg and Pavel A. Stoimenov. Based on a large data set comprising daily quotes of crude oil and natural gas futures, the authors estimate and model large comovements of commodity returns. To detect the presence of tail dependence a method based on the concept of tail copulas is applied, accounting for different scenarios of joint extreme outcomes. They provide an important discussion that includes some critical observations regarding the use of copulas for risk management purposes.
Finally, the fourth paper in the issue, "A note on panel hourly electricity prices" by Juan Ignacio Peña, looks at the interrelationships between hourly electricity prices in three day-ahead markets - the European Energy Exchange in Germany, the Paris Power Exchange in France and Operadora del Mercado Español de Electricidad in Spain - using a periodic panel model. The empirical results show that, for individual hourly price series, periodic autoregressive models fit the data better than standard autoregressive models and that, when all hourly prices are modeled jointly as a panel, such models fit the data better than standard nonperiodic models. The results have implications both for price modeling and for the management of electricity price risk in these markets. Thus, in the pricing of derivatives on hourly prices, it seems advisable to use the whole set of twenty-four hourly prices as the underlying process and not simply the prices for delivery at a specific hour, thereby providing support for the use of rainbow options.
Overall, these papers provide useful new methodological results in quantitative energy finance and a stimulus for further research in these areas - research that will, we hope, be included in a future issue of The Journal of Energy Markets.
Estimating a Lévy multifactor market model for electricity futures markets by using independent component analysis