Estimating value at risk using some estimators of the generalized pareto distribution under the peaks over threshold approach

Abstract EN

Extreme value theory (EVT) has two main approaches for dealing with extremes; the block maxima (BM) and the peaks over threshold approach (POT).

This paper focuses on the POT approach where the generalized Pareto distribution (GPD) is the limiting distribution for exceedances.

The GPD has many estimators for the scale and shape parameters.

A simulation study for comparing the performance of three new estimators, nonlinear least square (NLS), POT nonlinear least square (POT-NLS) and weighted nonlinear least square (WNLS), of the GPD under the peaks over threshold (POT) approach was conducted.

Different distributions which belong to the maximum domain of attraction of the GPD were considered for generating the data to study the effect of the deviationfrom the GPD and the effect of different sample sizes, threshold values (u) and quantile levels.

Then those estimates were used to calculate one of the common tail risk measures, the value at risk (VaR), for a heavy-tailed dataset.