A comparison study of pricing credit default swap index tranches with convex combination of copulae

Abstract

Copula as a tool for dependence modeling has been widely used in pricing portfolio-like financial derivatives, e.g. credit default swap index (CDX) tranches. Among the pricing models, the model equipped with the Gaussian copula has become the market benchmark for a long time. Albeit thereafter some other copulae were employed to improve the Gaussian model, yet a lot of them have suffered from shortcomings, especially in destitution of heterogeneous sectoral dependence, asymmetric dependence and fat tail dependence. For increasing the pricing accuracy and also keeping the model parsimonious, we propose in this paper an approach of convex combination of copulae (cc-copula) in pricing CDX tranches. Copulae from elliptical and Archimedean families were chosen as the components to construct the cc-copula models. In order to support the effectiveness of the cc-copula models, two distinct empirical studies were conducted to reproduce the spreads of the CDX tranches of two different contracts covering crisis and non-crisis periods. The results evince that the cc-copula based pricing models have dominant performance compared with the benchmark models.