Sensitivity Analysis of Value-at-Risk and Expected Shortfall to Copula Misspecification in CGMY Jump-Diffusion Models

Abstract

This study provides a comprehensive sensitivity analysis of risk measures to copula misspecification in CGMY jump-diffusion models, revealing substantial vulnerabilities in Value-at-Risk (VaR) and Expected Shortfall (ES) calculations. Using Monte Carlo simulation with 10,000 paths per scenario across multiple volatility regimes, jump intensities, and confidence levels, the study demonstrates that mean relative errors exceed 200% for VaR and 146% for ES when averaging across all six copula families including the severely misspecified Gumbel copula. Crucially, well-specified elliptical copulas exhibit bootstrap mean errors of only 1.5–2.3% for VaR and 2.0–2.3% for ES, while the Gumbel copula alone drives errors to 280.6% for VaR and 238.4% for ES in bootstrap-estimated means (corresponding to 1,190% and 839% in the worst individual scenarios), indicating that the aggregate averages are dominated by a single family’s structural failure rather than a pervasive property of the modelling framework. Two-way ANOVA confirms that both copula family (F = 3,614 for VaR; F = 5,192 for ES) and confidence level (F = 66 for VaR; F = 44 for ES) exert highly significant effects (all p < 2×10⁻¹⁰), while Tukey HSD post-hoc tests demonstrate that the Gumbel copula is the sole source of statistically distinguishable pairwise differences all five non-Gumbel copulas are statistically indistinguishable from one another at the 95% family-wise level. Contrary to expectation, low-volatility regimes exhibit the highest sensitivity to copula misspecification, while severe-jump regimes exhibit the lowest.