Energy-Related Commodity Futures: Statistics, Models and Derivatives

The objective of this thesis is a precise mathematical description of energy-related commodity futures markets with respect to risk management and derivative pricing. First, we provide a rigorous multivariate statistical analysis of important commodity futures prices including electricity, oil, coal, gas and CO2 emission allowances based on generalized hyperbolic distributions. We show how a straightforward calculation of expected shortfalls based on such distributions is possible and that the view on risks of energy portfolios is more realistic compared to Normal distributions. We are also able to show that the introduction of CO2 certificates can be used for risk reduction. Further, we build stochastic term-structure models for the electricity futures market based on a no-arbitrage theory stemming from delivery periods in the futures contracts. We discuss the performance of the model in the German electricity market based on Brownian motions and more general Lévy process. Moreover, we introduce pricing algorithms for options on electricity futures based on the above mentioned distributions and asses their performance.