Financial Modelling with Copulas: Model Selection for Risk Management
Authors
Kure, Sebastian Søndergaard ; Nørrevang, Rasmus Rosted
Term
4. term
Education
Publication year
2023
Submitted on
2023-06-01
Pages
74
Abstract
Amid heightened market volatility, this thesis investigates how copulas can be used to forecast portfolio risk and how to evaluate and select copula models for risk management. It outlines the theoretical foundations of copulas (including probability integral transforms, Sklar's theorem, examples, and tail dependence), details estimation and diagnostics (Bayesian estimation, goodness-of-fit testing, and marginal distribution modelling), and defines the key risk measures, Value-at-Risk and Expected Shortfall. The thesis describes a forecasting and backtesting procedure for these measures and employs a model confidence set to systematically identify models that are not statistically inferior to their competitors. The approach is illustrated on an equally weighted portfolio of NextEra Energy and British Petroleum through exploratory analysis, in-sample diagnostics, out-of-sample risk forecasts, and evaluation of forecast accuracy, culminating in the selection of superior copula model(s). While the excerpt does not report specific empirical rankings, the study provides a structured framework and practical guidance for risk managers seeking accurate dependence modelling and robust risk forecasts.
Dette speciale undersøger, hvordan copulaer kan bruges til at forudsige porteføljerisiko, og hvordan man evaluerer og udvælger copula-modeller til risikostyring i en tid med høj volatilitet. Arbejdet gennemgår de teoretiske grundlag for copulaer (herunder probability integral transforms, Sklar's sætning, eksempler og haleafhængighed), beskriver estimering og diagnostik (bayesiansk estimering, goodness-of-fit-test og modellering af marginalfordelinger) og definerer de centrale risikomål, Value-at-Risk og Expected Shortfall. Specialet skitserer en procedure for fremskrivning og tilbageprøvning af disse mål og anvender et model confidence set til systematisk at identificere modeller, der ikke er statistisk ringere end alternativerne. Tilgangen illustreres på en ligevægtet portefølje bestående af aktierne i NextEra Energy og British Petroleum gennem eksplorativ analyse, in-sample diagnostik, out-of-sample risikofremskrivninger og evaluering af prognosenøjagtighed, hvilket munder ud i udvælgelsen af bedre copula-modeller. Uddraget indeholder ikke specifikke empiriske rangeringer, men studiet tilbyder en struktureret ramme og praktisk vejledning til risikomanagere, der søger præcis afhængighedsmodellering og robuste risikoprognoser.
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