Gaussian and Poisson approximation: applications to CDOs tranche pricing

Nicole El Karoui, Ying Jiao, David Kurtz

Abstract

ABSTRACT

This paper describes a new numerical method, based on Stein’s method and zero bias transformation, of computing collateralized debt obligation (CDO) tranche prices. We propose first-order correction terms for both Gaussian and Poisson approximations, and the approximation errors are discussed. We then combine the two approximations to price CDO 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.