Vine Copulas For Multivariate Time Series Modelling, With An Application In Energy Finance
Translated title
Vine Copula Modeller For Tidsrækker, Med Anvendelse På Elmarkeder
Author
Valberg-Madsen, Janus Sejersbøll
Term
4. term
Education
Publication year
2019
Submitted on
2019-09-16
Pages
103
Abstract
This thesis develops a multivariate time series framework based on vine copulas and applies it to the German power market. It reviews copula theory, including Sklar’s theorem and key copula families, and shows how high-dimensional dependence structures can be built from bivariate copulas. After seasonal preprocessing, the marginal dynamics of day-ahead electricity prices, power consumption, and solar and wind generation are modeled with ARMA–GARCH, and an R-vine copula is estimated to capture their joint dependence. Using daily ENTSO-E data, the study quantifies how extreme weather scenarios propagate to prices; the analysis indicates that wind generation, in particular, has a strong impact on prices. Simulations from the fitted model are used to study the payoff distributions of portfolios of power purchase agreements linked to these variables, revealing long left tails and correspondingly large risk measures such as Value-at-Risk and expected shortfall. The study illustrates how vine copulas can support scenario analysis and risk assessment in energy finance.
Dette speciale udvikler en multivariat tidsserie-ramme baseret på vine-kopulaer og anvender den på det tyske elmarked. Vi gennemgår kopulateori, herunder Sklars sætning og centrale kopulafamilier, og viser, hvordan højdimensionelle afhængighedsstrukturer kan konstrueres af todimensionelle kopulaer. Efter sæsonkorrektion modelleres de marginale dynamikker for day-ahead elpriser, elforbrug samt sol- og vindproduktion med ARMA–GARCH, og en R-vine-kopula estimeres til at indfange den fælles afhængighed. Med daglige ENTSO-E-data kvantificeres, hvordan ekstreme vejrsituationer påvirker priser; analysen peger især på, at vindproduktion har en stærk effekt på prisdannelsen. Simulationer fra den estimerede model anvendes til at undersøge afkastfordelinger for porteføljer af power purchase agreements baseret på disse variable, hvilket afslører lange venstrehale og deraf store risikomål som Value-at-Risk og forventet shortfall. Studiet illustrerer, hvordan vine-kopulaer kan understøtte scenarieanalyse og risikovurdering i energifinans.
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Keywords
statistik ; copula ; vine copula ; elmarkeder ; elhandel