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| Teoria wartości ekstremalnych (EVT)× | Warunkowa wartość zagrożona (Oczekiwana strata)× | Wykładniczy GARCH (EGARCH)× | |
|---|---|---|---|
| Dziedzina≠ | Finanse | Finanse | Ekonometria |
| Rodzina | Regression model | Regression model | Regression model |
| Rok powstania≠ | 2001 | 2000 | 1991 |
| Twórca≠ | Coles (textbook treatment); McNeil, Frey & Embrechts | Rockafellar & Uryasev (2000); Acerbi & Tasche (2002) | Nelson |
| Typ≠ | Tail / extreme-event model | Coherent tail-risk measure | Conditional volatility model (asymmetric GARCH variant) |
| Źródło pierwotne≠ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 | Rockafellar, R. T. & Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2(3), 21-41. DOI ↗ | Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica, 59(2), 347-370. DOI ↗ |
| Inne nazwy≠ | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold | CVaR, expected shortfall, average value-at-risk, tail VaR | exponential GARCH, Nelson's EGARCH, asymmetric GARCH, EGARCH — Üstel GARCH |
| Pokrewne≠ | 5 | 5 | 4 |
| Podsumowanie≠ | 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. | Conditional Value-at-Risk (CVaR), also called Expected Shortfall, is a coherent tail-risk measure that quantifies the conditional expectation of losses beyond the Value-at-Risk threshold. It was introduced for optimization by Rockafellar and Uryasev (2000) and shown to be coherent by Acerbi and Tasche (2002), and it has replaced VaR as the regulatory standard under Basel III/IV. | 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. |
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