[Paper Review] Estimation of tail risk measures in finance: Approaches to extreme value mixture modeling

Yujuan Qiu|arXiv (Cornell University)|Jun 1, 2024

Financial Risk and Volatility Modeling16 references24 citations

TL;DR

The thesis surveys extreme value mixture models for tail risk in finance and shows that combining GARCH-preprocessed residuals with extreme value mixtures improves tail estimation over kernel-based methods.

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.

Motivation & Objective

• Evaluate extreme value mixture models and methods in finance and insurance settings.
• Review extreme value theory, time series behavior, volatility clustering, and risk measurement approaches.
• Assess the performance of extreme value mixture models across simulated distributions.

Proposed method

• Review and implement extreme value mixture models from the literature.
• Apply models to financial and insurance contexts using simulated distributions.
• Preprocess time series with GARCH and fit extreme value mixtures to the residuals.
• Compare kernel density estimation against other extreme value approaches in tail estimation.

Experimental results

Research questions

• RQ1 How do extreme value mixture models perform for estimating tail risk in finance and insurance?
• RQ2 Does kernel density estimation offer superior tail performance compared to other EVT-based methods?
• RQ3 Can GARCH preprocessing of time series residuals improve the fit and tail estimates when using EVT mixtures?
• RQ4 What are the strengths and limitations of extreme value mixture models in practical risk measurement?

Key findings

• Kernel density estimation does not have an absolute or near-best performance for extreme tails.
• Preprocessing data with GARCH and applying EVT mixture models to residuals improves goodness-of-fit.
• Extreme value mixture models can enhance tail distribution estimation relative to some baseline methods.
• The study provides comparative insights across different simulated distributions.