Elliptical and Archimedean copula models: an application to the price estimation of portfolio credit derivatives

Nneka Umeorah; Phillip Mashele; Matthias Ehrhardt

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We priced and conducted some comparative analysis on the impact of the elliptical and the Archimedean copula models on the pricing of the basket credit default swaps.
Based on the algorithm computational time in the valuation process, the Gumbel copula outperformed other copula models in the Archimedean class, and the Student t copula proved to be more computationally expensive in the elliptical class.
Finally, using a lower degree of freedom, the Student t copula resulted in nonmonotonic results of the swap valuation, and when the degree of freedom was increased drastically, a monotonic result was obtained which, in turn, coincided with the Gaussian copula results.

Abstract

This paper explores the impact of elliptical and Archimedean copula models on the valuation of basket default swaps. We employ Monte Carlo simulation, in connection with the copula models, to estimate the default times and to calculate the swap payment legs and the cumulative swap premium. The numerical experiments reveal some sensitivity analysis on the impact of swap parameters on the fair prices of the nth-to-default swaps. Finally, using the results presented, an appropriate choice of copula model can be made based on the computation time of the valuation process, and such a choice hugely affects the quantitative risk analysis of the portfolio.

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