Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor

Dr. Matt Davison, Dr. Lindsay Anderson

Abstract

Due to climate change concerns, high oil prices and nuclear dangers there is increasing support for renewable energy. At the forefront of the debate for government support of renewable energy are wind energy and biofuels. Used primarily for power generation and transportation, respectively, there have been many debates surrounding the reliability and efficiency of these resources. These debates often address the uncertainty in the economic value of the resource through time, however it is often difficult to quantify this uncertainty, which stems from the random behavior of prices and the unpredictable nature of the resource itself.

In this thesis we use well developed theory taken from quantitative finance, more specifically real options theory, as well as various mathematical and statistical techniques and models used in option pricing to determine the economic value of these resources. Market design and policy are key considerations throughout the analysis. A simplified model of a corn ethanol plant is analyzed using a simple Margrabe exchange option as well as numerical techniques such as bootstrapping and finite difference methods for solving partial differential equations. It is determined that, as correlation between corn price and gasoline price increases, the value of the ethanol plant decreases. The level of decrease is substantial, and the economic and political consequences are discussed.

A simplified wind-storage model is also developed and analyzed as a dynamic program, allowing for analytic solutions. This allows for the determination of an optimal bidding strategy when the penalty for failing to meet a committed generation level is defined. The market consequences of these results are discussed and compared with numerical results obtained from a more complex wind-storage model where analytical solutions are not available. These results are obtained using a modified block bootstrapping method, and the optimal storage size is determined for a specific penalty structure.


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