Copula Analysis of Risk: A Multivariate Risk Analysis for VaR and CoVaR using Copulas and DCC-GARCH

ArXiv ID: 2505.06950 “View on arXiv”

Authors: Aryan Singh, Paul O Reilly, Daim Sharif, Patrick Haughey, Eoghan McCarthy, Sathvika Thorali Suresh, Aakhil Anvar, Adarsh Sajeev Kumar

Abstract

A multivariate risk analysis for VaR and CVaR using different copula families is performed on historical financial time series fitted with DCC-GARCH models. A theoretical background is provided alongside a comparison of goodness-of-fit across different copula families to estimate the validity and effectiveness of approaches discussed.

Keywords: Value at Risk (VaR), Conditional Value at Risk (CVaR), Copula Families, DCC-GARCH, Multivariate Risk Analysis, General Financial Assets

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents dense mathematical theory including copulas, DCC-GARCH, and probability transforms, while also detailing a structured empirical methodology with backtesting and goodness-of-fit comparisons.

  flowchart TD
    Start["Research Goal<br>Multivariate Risk Analysis<br>for VaR & CoVaR"] --> InputData["Input: Historical<br>Financial Time Series"]
    InputData --> DCCGARCH["DCC-GARCH<br>Model Fitting<br>(Volatility & Correlation)"]
    DCCGARCH --> Residuals["Output:<br>Standardized Residuals"]
    Residuals --> CopulaFit["Copula Fitting<br>(Gaussian, Student-t, etc.)"]
    CopulaFit --> Analysis["Analysis:<br>Risk Metrics Calculation<br>VaR & CoVaR Estimation"]
    Analysis --> Comparison["Goodness-of-Fit<br>Comparison<br>Across Copula Families"]
    Comparison --> Findings["Key Findings:<br>Optimal Copula Selection<br>& Risk Model Validity"]