On a multivariate extension for Copula-based Conditional Value at Risk

ArXiv ID: 2508.16132 “View on arXiv”

Authors: Andres Mauricio Molina Barreto

Abstract

Copula-based Conditional Value at Risk (CCVaR) is defined as an alternative version of the classical Conditional Value at Risk (CVaR) for multivariate random vectors intended to be real-valued. We aim to generalize CCVaR to several dimensions (d>=2) when the dependence structure is given by an Archimedean copula. While previous research focused on the bivariate case, leaving the multivariate version unexplored, an almost closed-form expression for CCVaR under an Archimedean copula is derived. The conditions under which this risk measure satisfies coherence are then examined. Finally, numerical experiments based on real data are conducted to estimate CCVaR, and the results are compared with classical measures of Value at Risk (VaR) and Conditional Value at Risk (CVaR).

Keywords: Copula-based Conditional Value at Risk, Archimedean copula, Coherent risk measure, Multivariate risk measure, Value at Risk, General Equities/Portfolio Risk

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper develops a novel multivariate generalization of a risk measure using Archimedean copulas, requiring advanced multivariate calculus and distribution theory. While it includes real data numerical experiments for validation, the implementation details are not provided, and the methodology is more theoretical than fully backtest-ready.

  flowchart TD
    A["Research Goal:<br>Generalize CCVaR to d>=2<br>with Archimedean Copula"] --> B["Key Methodology:<br>Derive multivariate CCVaR<br>using conditional inversion"]
    B --> C["Data Input:<br>Real Financial Data<br>General Equities/Portfolio"]
    C --> D{"Computational Process"}
    D --> E["Calculate VaR & CVaR<br>Baseline Measures"]
    D --> F["Estimate CCVaR<br>via Archimedean Copula"]
    D --> G["Check Coherence<br>Properties"]
    E --> H["Key Findings:<br>1. Closed-form multivariate CCVaR<br>2. Coherence conditions defined<br>3. CCVaR vs. VaR/CVaR comparison"]
    F --> H
    G --> H