Copula sensitivity analysis for portfolio credit derivatives

Abstract

Modeling dependence among input random variables is often critical for performance evaluation of stochastic systems, and copulas provide one approach to model such dependence. In the financial industry, the dependence among default times of different assets drives the pricing of portfolio credit derivatives, including basket default swaps and collateralized debt obligations. Copula sensitivities provide information about how changes in the dependence level affect the output. We study sensitivity analysis of elliptical copulas and Archimedean copulas using infinitesimal perturbation analysis, and an unbiased estimators is derived using conditional Monte Carlo (CMC) to address discontinuities that arise in portfolio credit derivatives. In simulation experiments, the new estimators have smaller variance than other applicable methods.