A Comparative Analysis of Basket Default Swaps Pricing Using the Stein Method

Abstract

Using the Stein numerical method, introduced by El Karoui and Jiao {ElKJ} and El Karoui, Jiao and Kurtz {ElKJK}, we compare, in terms of accuracy and efficiency, the pricing of the basket default swaps (NTDs and CDO Tranches). In the Factor Copula Model framework, we compare the following copula functions: 1 factor and 3 factors Gaussian copula, Clayton copula, Marshall-Olkin copula, Double-t copula and Student copula. Stein numerical method is also compared with the Recursive method of Hull and White, with the Probability Generating Function method (an exact Fourier transform like method) and with the Monte Carlo method.