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

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.