This thesis consists of an introduction as well as four papers. The papers
concern different problems associated to future electricity markets and the
topics include risk management, investment strategies, valuation and model
calibration. Each paper is presented in a separate chapter and hence the
chapters are self-contained and may be read individually. A more thorough
overview is presented in Chapter 1.
In Chapter 2 we consider a hedging problem for a power distributor delivering
electricity on fixed price contracts in the Nordic electricity market and
thereby being exposed to volume risk. We develop time series models for the
electric load, system price and deviation from system price. The model is
designed such that for independent electric load, system price and deviations
from system price, the minimal variance hedge coincide with the standard
practice of the industry. We extend the model to include price and load correlation
which results in an explicit strategy that reduces the variance. To
further improve the strategy we include autocorrelation and solve the hedging
problem numerically and show that there is a large potential in changing risk
measure and utilizing the skewness in the payoff distribution.
In Chapter 3 we consider an investment problem for a strategic investor
and a social planner with the opportunity to invest in inflexible and flexible
generation. We study the impact of market power and conjectured market
changes with a simple price model based on linear demand response. We show
that the strategic investor invests later and in less capacity than the socially
optimal and that with increased market ownership investment is delayed further
and capacity increased slightly. Furthermore, we find that an increase in
market share for the strategic investor delays inflexible generation more than
flexible generation due to the exposure to potential low prices.
In Chapter 4 we study the valuation of three representative generation
types, an inflexible wind turbine, a flexible gas fired power plant and a hydroelectric
plant that allows for storage. We account for the special characteristics
of each technology and include uncertainty in both price and volume
through diffusion or jump diffusion models. We find explicit expressions for
the expected instantaneous value of wind generation as a function of electricity
price and wind speed. We include startup and shutdown costs for the gas
fired power plant determine the startup and shutdown triggers as well as the
value of the plant by maximizing the value of shutting down. This is done analytically
in the diffusion models and numerically in the jump diffusion model.
For the hydroelectric power plant we relax storage level and discharge constraints
using penalty functions and linearize the optimal strategy from the
Hamilton-Jacobi-Bellman equation. This allows for closed form expressions of
the value in terms of the expected price, the second moment of the price and
the autovariance of the price. We calibrate the models to 7 years of hourly
price and wind data, determine the value and study the impact of anticipated
market changes on the value of the three types of generation.
In Chapter 5 we develop an EM-algorithm with two jump components
such that the jump density of the compound Poisson process is a mixture
of two normal distributions. We show that each step of the EM-algorithm
increases the log-likelihood of the observed data by maximizing the expectation
of the log-likelihood for the complete data conditional on the observed
data. We determine explicit expressions for the maximization step in terms
of simple conditional expectations and present an approach for determining
the conditional expectations. Finally, by applying the algorithm to calibrate
the jump diffusion model from Chapter 4, we demonstrate that the additional
jump component provides a significantly better model of the observed data
than a model without jumps and with only a single jump component.