We consider a factor approach to the pricing of basket credit derivatives and synthetic CDO tranches. Our purpose is to deal in a convenient way with dependent defaults for a large number of names. We provide semi-explicit expressions of the stochastic intensities of default times and pricing formulae for basket default swaps and CDO tranches. Two cases are studied in detail: mean-variance mixture models and frailty models. We also compare prices under Gaussian and Clayton copulas. The …rst version circulated as in internal BNP Paribas working paper in may 2001; a second version has been disclosed on the web in october 2002. The authors thank D. Du¢e, C. Gouriéroux, M. Musiela, members of the credit derivative research team at BNP Paribas and participants at the Quantitative Finance RISK conference, the Credit Derivatives RISK seminar, the Bachelier seminar on default risk held at University of Evry, the French Finance Association and Quant'03 conferences. We also thank X. Burtschell for computational assistance. The usual disclaimer applies.1 See Junker and Ellis [1998] for some characterizations of one factor models and Gouriéroux and [2002] for some application to credit risk.
Monfort
SURVIVAL FUNCTIONS AND STOCHASTIC INTENSITIESP Ni] (L(t)). Equity and senior tranches are treated similarly. We can notice that M (t) is a pure jump process derived from L(t). We will thereafter denote M (t) = !(L(t)) where ! is non decreasing function.The holder of a synthetic CDO tranche receives at time T a unique principal payment of M (1)¡M (T ), where M (1) denotes the initial nominal of the tranche and M (1) ¡ M(t) will thereafter denote the outstanding 22 Or on plain Credit Default Swaps. 23 In order to simplify notations, we use a unique terminology M (t) to denote the cumulative losses on the three tranches.
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