Price modelling and asset valuation in carbon emission and electricity markets

Thesis

This thesis is concerned with the mathematical analysis of electricity and carbon emission markets.

We introduce a novel, versatile and tractable stochastic framework for the joint price formation of electricity spot prices and allowance certificates. In the proposed framework electricity and allowance prices are explained as functions of specific fundamental factors, such as the demand for electricity and the prices of the fuels used for its production. As a result, the proposed model very clearly captures the complex dependency of the modelled prices on the aforementioned fundamental factors. The allowance price is obtained as the solution to a coupled forward-backward stochastic differential equation. We provide a rigorous proof of the existence and uniqueness of a solution to this equation and analyse its behaviour using asymptotic techniques. The essence of the model for the electricity price is a carefully chosen and explicitly constructed function representing the supply curve in the electricity market.

The model we propose accommodates most regulatory features that are commonly found in implementations of emissions trading systems and we analyse in detail the impact these features have on the prices of allowance certificates. Thereby we reveal a weakness in existing regulatory frameworks, which, in rare cases, can lead to allowance prices that do not conform with the conditions imposed by the regulator.

We illustrate the applicability of our model to the pricing of derivative contracts, in particular clean spread options and numerically illustrate its ability to "see" relationships between the fundamental variables and the option contract, which are usually unobserved by other commonly used models in the literature.

The results we obtain constitute flexible tools that help to efficiently evaluate the financial impact current or future implementations of emissions trading systems have on participants in these markets.

Authors: Schwarz, D

• Publication date: 2012
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Forward-Backward Stochastic Differential Equation; Electricity; Commodity Market; Derivative Pricing; Emission Market; Non-linear Partial Differential Equation
• Subjects: Mathematics; Probability theory and stochastic processes; Mathematical finance