Impact of Copula Misspecification on Option Pricing Accuracy in CGMY Jump-Diffusion Models: A Comprehensive Analysis

Abstract

This study presents a comprehensive analysis of how copula misspecification affects option pricing accuracy in jump-diffusion models incorporating Carr-Geman-Madan-Yor (CGMY) jumps. Using Monte Carlo simulation with 10,000 paths per scenario across 324 scenarios spanning six copula specifications, four jump intensity regimes, three correlation levels, three maturities, and three interest rate environments, the study reveals a striking three-order-of-magnitude performance hierarchy between copula families. Elliptical copulas (Gaussian, t-copulas with df ∈ {3, 5, 8}) demonstrate exceptional robustness with mean relative pricing errors below 0.23%. In contrast, Archimedean copulas (Clayton, Gumbel) exhibit catastrophic failure, with mean errors of 666.0% and 1,548.0% respectively. These errors arise from fundamental structural incompatibility between Archimedean tail-dependence architectures and the symmetric, infinite-activity nature of CGMY jump processes, confirmed by three diagnostic criteria. A paradoxical ‘misspecification valley’ is observed at mild jump intensity, where errors peak above those under both no-jump and severe-jump conditions. The t-copula with eight degrees of freedom achieves the lowest mean error (0.218%), while the t-copula with three degrees of freedom provides superior robustness with the lowest coefficient of variation (0.847). Statistical validation via three-way ANOVA confirms that copula family explains 68.47% of total pricing error variance compared to 3.2% for all CGMY parameters combined.