Energy-related commodity futures - statistics, models and derivatives

Abstract

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. On the other hand, 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. In a separate simulation study, we give new insight into the pricing of Asian options via distributional approximations. We assess the commonly used lognormal approximation, the more recent alternative of a Normal inverse-Gaussian approximation and a distribution proposed by us, the exponential of a Normal inverse-Gaussian distribution. We show that the proposed exponential of a Normal inverse-Gaussian distribution improves alternative approximations in multiple respects. It does not only advance the quality of the tail-behavior of the approximation, it also stays positive (in contrast to the Normal inverse-Gaussian candidate). Further, it is flexible enough to yield an overall fit of the true distribution that makes the two almost indistinguishable in some cases. The new option pricing algorithms stemming from the study are already applied in the previous chapters for pricing options on electricity futures.