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| Miary ryzyka ogona (Expected Shortfall, spektralne, ekspotencjalne)× | Teoria wartości ekstremalnych (EVT)× | |
|---|---|---|
| Dziedzina | Finanse | Finanse |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1999 | 2001 |
| Twórca≠ | Artzner, Delbaen, Eber & Heath (coherent risk axioms); Acerbi & Tasche (Expected Shortfall) | Coles (textbook treatment); McNeil, Frey & Embrechts |
| Typ≠ | Coherent tail risk measure | Tail / extreme-event model |
| Źródło pierwotne≠ | Artzner, P., Delbaen, F., Eber, J.-M. & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203–228. DOI ↗ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 |
| Inne nazwy≠ | expected shortfall, conditional value at risk, CVaR, spectral risk measure | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold |
| Pokrewne | 5 | 5 |
| Podsumowanie≠ | Tail risk measures quantify the loss distribution beyond Value-at-Risk (VaR). Expected Shortfall — the expected loss given that VaR is exceeded — is the leading coherent risk measure, formalised by Artzner, Delbaen, Eber and Heath (1999) and shown to be coherent by Acerbi and Tasche (2002). Spectral and expectile-based measures generalise it. | 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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