Linganisha mbinu

	Nadharia ya Thamani Iliyokithiri (EVT)	Thibitisho la Thamani ya Hatari (Matarajio ya Upungufu)	Nadharia ya Hisa Zinazotambulika na Muundo wa HAR
Nyanja	Fedha	Fedha	Fedha
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2001	2000	2009
Mwanzilishi	Coles (textbook treatment); McNeil, Frey & Embrechts	Rockafellar & Uryasev (2000); Acerbi & Tasche (2002)	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)
Aina	Tail / extreme-event model	Coherent tail-risk measure	Time-series regression of realized variance
Chanzo asilia	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.	Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174-196.
Majina mbadala	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold	CVaR, expected shortfall, average value-at-risk, tail VaR	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV
Zinazohusiana	5	5	5
Muhtasari	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.	Realized volatility estimates an asset's variance directly from high-frequency intraday returns rather than from a parametric latent process. The Heterogeneous Autoregressive (HAR) model of Corsi (2009), building on the realized-volatility framework of Andersen, Bollerslev, Diebold and Labys (2003), forecasts this measure by combining daily, weekly, and monthly volatility components, and is a strong alternative to GARCH for volatility prediction.