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| Kopula-Modelle (Gauß, t, Clayton, Gumbel, Frank)× | Exponential GARCH (EGARCH)× | Extremwerttheorie (EVT)× | |
|---|---|---|---|
| Fachgebiet≠ | Finanzwirtschaft | Ökonometrie | Finanzwirtschaft |
| Familie | Regression model | Regression model | Regression model |
| Entstehungsjahr≠ | 1959 | 1991 | 2001 |
| Urheber≠ | Sklar (1959); dependence-concept treatment by Joe (1997) | Nelson | Coles (textbook treatment); McNeil, Frey & Embrechts |
| Typ≠ | Dependence model | Conditional volatility model (asymmetric GARCH variant) | Tail / extreme-event model |
| Wegweisende Quelle≠ | Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut Statistique de l'Université de Paris, 8, 229-231. link ↗ | Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370. DOI ↗ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 |
| Aliasnamen≠ | copulas, dependence copulas, vine copulas, Kopula Modelleri (Gaussian, t, Clayton, Gumbel, Frank) | exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold |
| Verwandt≠ | 5 | 4 | 5 |
| Zusammenfassung≠ | Copula models are a family of functions that describe the dependence structure between variables separately from their individual (marginal) distributions. The foundation is Sklar's theorem (1959), which shows that any multivariate distribution can be split into its marginals plus a copula; Joe (1997) developed the modern catalogue of dependence concepts. They are central to portfolio risk and credit modelling. | EGARCH is an asymmetric GARCH variant, introduced by Nelson in 1991, that models the leverage effect in which bad news raises volatility more than good news of the same size. It captures the negative-shock asymmetry of financial return series by modelling the logarithm of the conditional variance. | Extreme Value Theory is a statistical framework for modelling the rare events that live in the tail of a probability distribution. As developed in Coles (2001) and applied to risk by McNeil, Frey & Embrechts (2005), it offers two standard routes: the Generalized Extreme Value (GEV) distribution for block maxima and the Generalized Pareto Distribution (GPD), used in the peaks-over-threshold approach, for exceedances above a high threshold. |
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