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| Kopula-Modelle (Gauß, t, Clayton, Gumbel, Frank)× | Extremwerttheorie (EVT)× | |
|---|---|---|
| Fachgebiet | Finanzwirtschaft | Finanzwirtschaft |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1959 | 2001 |
| Urheber≠ | Sklar (1959); dependence-concept treatment by Joe (1997) | Coles (textbook treatment); McNeil, Frey & Embrechts |
| Typ≠ | Dependence model | 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 ↗ | 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) | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold |
| Verwandt | 5 | 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. | 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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