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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

Since the beginning of the credit and liquidity crisis, financial institutions have been considering creating a convertible-bond type contract focusing on capital. Under the terms of this contract, a bond is converted into equity if the authorities deem the institution to be under-capitalized. This paper discusses this contingent capital (CoCo) bond instrument and presents a pricing methodology based on firm value models that calibrate exactly the credit term structure of the issuer either through credit default swaps or corporate bonds data. Decorrelation between the capital conversion trigger and credit quality is introduced. The equity value for the issuer is derived in closed form with a barrier option type formula. A stress test of model parameters is illustrated to account for potential model risk and the obtained prices are compared to the price obtained from a market source. Finally, a brief overview of how the instrument valuation performs compared to pure corporate bonds and a discussion involving the CDS bond basis are presented.