Threshold Exceedances: Generalized Pareto Distribution

This lecture covers the concept of threshold exceedances, focusing on the Generalized Pareto Distribution (GPD). It explains how the method of block maxima is inefficient compared to threshold exceedances, which capture extreme data points above a specified level. The GPD is highlighted as the main distribution for modeling exceedances over a threshold, with discussions on distribution functions and properties. The lecture also delves into the excess distribution over a threshold, mean excess function, and implications of the GPD model. Various examples and models are presented to illustrate the application of GPD in analyzing excess losses and credit risk.