Polynomial Maps of Polynomial Processes for Energy Markets

Sun, Zuming

Polynomial Maps of Polynomial Processes for Energy Markets

dc.contributor.advisor	Ware, Antony
dc.contributor.author	Sun, Zuming
dc.contributor.committeemember	Ware, Antony
dc.contributor.committeemember	Aïd, René
dc.contributor.committeemember	Shaffer, Blake
dc.contributor.committeemember	Swishchuk, Anatoliy
dc.contributor.committeemember	Qiu, Jinniao
dc.date	2025-02
dc.date.accessioned	2024-12-05T21:37:05Z
dc.date.available	2024-12-05T21:37:05Z
dc.date.issued	2024-12-05
dc.description.abstract	The empirical evidence reveals that energy prices are different from other commodity prices, exhibiting seasonality, mean reversion and extremely high volatility. These features arise from the interaction between supply and demand, with each subject to seasonal variations, and in particular from constraints on storage, transmission or transportation, perhaps exacerbated by sudden changes due to unforeseen infrastructure breakdowns. Pricing energy assets and energy derivatives is a significant challenge. In this thesis, we present a modeling framework based on the mathematical foundations for polynomial diffusions, involving polynomial maps of polynomial processes (PMPP models) for various energy prices such as oil, natural gas and electricity prices. Under the PMPP framework, underlying factors are modeled by polynomial processes such as the Ornstein-Uhlenbeck process, geometric Brownian motion, inhomogeneous geometric Brownian motion and etc. Energy prices are generated by polynomial maps of these underlying processes. The polynomial maps can be determined either by monotone polynomial maps or regression, revealing the relationship between underlying factors and energy prices. We will show that PMPP models are able to describe the dynamics of spot and forward prices in energy markets, providing the advantage of cheap and convenient computation of forward prices because of the property of polynomial processes that the conditional expectations of polynomial functions of future states, conditional on current states, are given by polynomials of the current states. We also introduce a potential extension of the PMPP framework where the underlying factor process and the map may not be polynomial. Under this extended framework, the PMPP model will still reserve a quasi-polynomial property whereby conditional expectation of polynomial functions of the future state are given by functions of the current state in a space spanned by a finite set of basis functions. The optimal PMPP model is determined by the statistical criteria. The maximum likelihood estimation and Kalman filters are applied for model calibration. Preliminary results indicate that the PMPP models are able to capture the behavior of energy prices well and can be useful for risk management purposes.
dc.identifier.citation	Sun, Z. (2024). Polynomial maps of polynomial processes for energy markets (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.uri	https://hdl.handle.net/1880/120161
dc.language.iso	en
dc.publisher.faculty	Graduate Studies
dc.publisher.institution	University of Calgary
dc.rights	University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subject	Energy Markets
dc.subject	Polynomial Processes
dc.subject	Polynomial Maps
dc.subject	Gas Prices
dc.subject	Oil Prices
dc.subject	Power Prices
dc.subject	Forward Prices
dc.subject	Volatility Analysis
dc.subject.classification	Education--Mathematics
dc.title	Polynomial Maps of Polynomial Processes for Energy Markets
dc.type	doctoral thesis
thesis.degree.discipline	Mathematics & Statistics
thesis.degree.grantor	University of Calgary
thesis.degree.name	Doctor of Philosophy (PhD)
ucalgary.thesis.accesssetbystudent	I do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.