Statistics of Extreme Risks

Objectifs

The aim of this course is to study the statistical methods inherent in the measurement of extreme risks and to apply various parametric models to the estimation of Value-at-Risk. In this context, extreme value theory and conditional volatility models (GARCH) will be used to determine precise Value-at-Risk.

Plan

1. Value-at-Risk: foundations and first formalizations
1.1 Basics of VaR
1.2 Non-parametric methods
1.3 Parametric modeling

2. Value-at-Risk and modeling extremes
2.1. Block maxima modeling
2.2 Excess distribution modeling
2.3 Static Value-at-Risk
2.4 Dynamic Value-at-Risk

Prérequis

Extreme value theory, statistical inference, GARCH model