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

ArXiv ID: 2407.05933 “View on arXiv”

Authors: Unknown

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.

Keywords: Extreme Value Theory, Mixture Models, GARCH, Risk Measurement, Time Series Analysis

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical theory including extreme value theory, mixture models, and GARCH modeling, supported by rigorous derivations. It is evaluated on simulated data and real financial datasets with performance metrics, though it lacks a live trading strategy or specific backtest results.

  flowchart TD
    A["Research Goal<br/>Estimate Tail Risk in Finance<br/>using Extreme Value Mixture Models"] --> B["Data & Input<br/>Simulated Distributions &<br/>Financial Time Series Data"]
    B --> C{"Methodology Choice"}
    C --> D["Approach 1: Direct Mixture Modeling<br/>Apply models directly to raw data"]
    C --> E["Approach 2: GARCH Preprocessing<br/>Fit GARCH model to handle volatility clustering"]
    E --> F["Extract Residuals<br/>(Standardized Data)"]
    F --> G["Apply Mixture Models<br/>on Residuals"]
    D --> H{"Computational Comparison"}
    G --> H
    H --> I["Key Outcomes & Findings"]
    I --> J["1. Kernel Density Estimation (KDE)<br/>Not consistently superior for extremes"]
    I --> K["2. GARCH + Residual Modeling<br/>Improves goodness of fit &<br/>tail estimation accuracy"]
    I --> L["3. Tail Risk Metrics<br/>VaR/ES estimated robustly via<br/>Extreme Value Theory"]