Disputas: Hanna Marta Zdanowicz
M. Sc. Hanna Marta Zdanowicz ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:
Pricing and hedging in energy markets with weather factor risk
Hanna Marta Zdanowicz
Tid og sted for prøveforelesning
Førsteamanuensis Elisa Nicolato, Aarhus University
Professor Hans Julius Skaug, Universitetet i Bergen
Førsteamanuensis Ingrid Hobæk Haff, Universitetet i Oslo
Leder av disputas
Professor Tom Louis Lindstrøm, Matematisk institutt, Universitetet i Oslo
- Professor Fred Espen Benth, Matematisk institutt, Universitetet i Oslo
- Lecturer Almut Elisabeth Dorothea Veraart, Matematisk institutt, Imperial College London
Weather has a great direct influence on electricity from both a supply and demand point of view. For example, a cold winter means a greater demand for heating whereas large volumes of rain and snow provide water to the reservoirs for hydropower production. Moreover, other factors, like gas and coal prices or carbon emission certificates, have impact on electricity prices via production costs. The renewable energy producers receive operating subsidies in order to stimulate the development of this category; at the same time the traditional power producers are penalised and their operating costs are increased by the carbon emission certificates. All of this translates into a need for risk management tools capable of hedging against weather conditions directly and indirectly through unfavorable changes in prices. Such tools can be options written on the spread between the electricity price and the fuel price and financial instruments based on weather indices.
In this thesis we consider spread options with bivariate geometric Brownian dynamics with time-varying parameters. We extend several approximation methods to this model and develop a pricing method based on the Taylor expansion. We also work with a rich class of volatility modulated Volterra (VMV) processes as the price dynamics. These processes are important in modelling energy markets as they can capture the characteristics like spikes in prices and stochastic volatility. We derive the price of a spread option based on two commodities with dynamics described by a bivariate VMV process. We compute the quadratic hedge for the spread option. We illustrate the theory with numerical examples.
We tackle the problem of finding simple models that can describe solar power production accurately by time series methods without including additional weather related regressors. We compare the output from the models with forecasts provided by the producers. The study reveals that models work very well compared to rather complex models used by the TSOs. We conclude that the approach of modelling photovoltaic power generation by time series methods can be useful and provides valuable insight into the market.
Lastly, we extract smooth CAT curves from the finite set of CDD and HDD prices quoted at the CME. We find a theoretical functional connection between CATs and CDDs/HDDs in case of Orstein-Uhlenbeck temperature dynamics and use the Nelson-Siegel parametrisation to model the CAT curve. We calibrate the curve and then recover the CDD/HDD prices. We show empirically that after including the seasonality function in the parametrisation, the original Nelson-Siegel curve reduces to a constant.
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