Estimation of tail risk measures in finance: Approaches to extreme value mixture modeling

TL;DR

This thesis reviews and compares extreme value mixture models for tail risk estimation in finance, highlighting the impact of data preprocessing with GARCH models on model performance.

Contribution

It provides a comprehensive evaluation of various extreme mixture models and demonstrates how GARCH preprocessing enhances tail risk estimation accuracy.

Findings

Kernel density estimation methods do not consistently outperform others.

Preprocessing with GARCH improves tail distribution fitting.

GARCH residuals lead to better tail risk estimates.

Abstract

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series, volatility clustering, and risk measurement methods in detail. Comparing the performance of extreme mixture models and methods on different simulated distributions shows that the method based on kernel density estimation does not have an absolute superior or close to the best performance, especially for the estimation of the extreme upper or lower tail of the distribution. Preprocessing time series data using a generalized autoregressive conditional heteroskedasticity model (GARCH) and applying extreme value mixture models on extracted residuals from GARCH can improve the goodness of fit and the estimation of the tail distribution.