Optimal exercise of swing contracts in energy markets: an integral constrained stochastic optimal control problem
Matteo Basei (University of Padova, Italy)
Joint work with Annalisa Cesaroni and Tiziano Vargiolu

Thursday June 5, 11:30-12:00 | session 7.7 | Energy Finance | room I

We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with strict constraints gives rise to a stochastic control problem with a nonstandard state constraint. We approach this problem by a penalty method: we consider a general constrained problem and approximate the value function with a sequence of value functions of appropriate unconstrained problems with a penalization term in the objective functional. Coming back to the case of swing contracts with strict constraints, we finally characterize the value function as the unique viscosity solution with polynomial growth of the HJB equation subject to appropriate boundary conditions.

A Structural Model for Coupled Electricity Markets
Michael Kustermann (Universität Duisburg-Essen, Germany)
Joint work with Rüdiger Kiesel

Thursday June 5, 12:00-12:30 | session 7.7 | Energy Finance | room I

Structural or hybrid models for electricity prices are models, in which supply and demand of electricity are modelled explicitly. The electricity price is then (as in classical microeconomic theory) given as the intersection of supply and demand. These models have become very popular for electricity spot prices due to the fact that the risk factors driving supply and demand are better understood and easier observable than in most other markets. However, one very important risk factor - import and export - could not be modeled endogenously in such a model. We propose a multi-market extension of the class of Structural models which is able to capture the subtle interplay between separated but coupled electricity markets. Electricity markets are said to be coupled, if they are interconnected and the interconnector capacity is used such that market price differences are minimized. Our model leads to closed form formulae for futures and option prices. Interestingly, it turns out that futures prices in coupled markets might be lower than the lowest corresponding futures price in the same markets without interconnector capacity.

Modelling Electricity Prices By Brownian Semistationary Processes
Mikkel Bennedsen (Aarhus University, Denmark)
Joint work with Asger Lunde and Mikko Pakkanen

Thursday June 5, 12:30-13:00 | session 7.7 | Energy Finance | room I

In this paper we introduce Brownian Semistationary ($\mathcal{BSS}$) processes as a model for electricity prices. The $\mathcal{BSS}$ framework generalizes the often used Schwartz model and accounts for several stylized facts in commodity markets. In particular, it allows us to model (de-seasonalized) price levels directly in stationarity, to fit a general autocovariance structure of empirically observed prices and to capture time varying volatility and volatility clustering through a stochastic volatility component. We present estimators of the parameters in the model and investigate their finite sample performances. The estimator of the so-called \emph{smoothness parameter} of a $\mathcal{BSS}$ will allow us to examine the smoothness of the paths of our prices and we in this way devise a test for semimartingality of the price process. We apply these methods to the Nordic electricity market Nordpool and explore the properties of the electricity spot prices, where we find that the paths of the hour-by-hour (day ahead) prices are rougher than the Schwartz model would suggest and in particular that the price processes are \emph{not necessarily semimartingales.}