In this paper we investigate one‐factor models that extend the classical Gaussian copula model for pricing tranches of CDOs. We introduce Lévy base correlation and compare it to the classical Gaussian copula. The results of a historical study of both models on the iTraxx Europe Main dataset are presented. Our focus is on the base correlation surface and on the deltas of the tranches with respect to the index. We observe that the Lévy base correlation curve is much flatter than the corresponding Gaussian one. With respect to the deltas we conclude that the Lévy model produces larger deltas for the equity tranche and smaller deltas for the senior tranches. Copyright © 2009 Wilmott Magazine Ltd

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The normal inverse Gaussian (NIG) process is a Lévy process with no Brownian component and NIG‐distributed increments. The NIG process can be constructed either as a process with NIG increments or, alternatively, via random time change of Brownian motion using the inverse Gaussian process to determine time. The article presents the normal inverse Gaussian distribution function and the corresponding characteristic function and Lévy measure. Further, the NIG process is used to construct a market model for financial assets. Option pricing can be done using the NIG density function, the NIG Lévy characteristics, or the NIG characteristic function.