Gauss and Poisson approximation: applications to CDO tranches pricing

Nicole El Karoui (1) , Ying Jiao (2) , David Kurtz (3)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 BlueCrest Capital Management Limited

This article describes a new numerical method, based on Stein's method and zero bias transformation, to compute CDO tranche prices. We propose first order correction terms for both Gauss and Poisson approximations. We then combine the two approximations to price CDOs tranches in the conditionally independent framework using a realistic local correlation structure. Numerical tests show that the method provides robust results with a very low computational burden.

Domaines: Probabilités [math.PR]

Nicole El Karoui, Ying Jiao, David Kurtz. Gauss and Poisson approximation: applications to CDO tranches pricing. 2008. ⟨hal-00324208⟩