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We study the risk of CDO^sup 2^ and, more precisely, we highlight the complex relationships between the dependence structure of the underlying assets packaged in the inner CDOs, the level of subordination of the singletranche CDOs, and the performance of the single-tranche CDO^sup 2^ (ST CDO^sup 2^) itself. These new credit derivatives are typically leveraged single-tranche CDOs (the master CDO or outer CDO) in which the underlying assets are CDO tranches (the inner CDOs) or a mixture of CDO tranches and ABS. The performance of the single-tranche CDO^sup 2^ (ST CDO^sup 2^) is derived from the performance of the pool of single-tranche CDOs (ST CDOs), which in turn depends on the performance of the combined pools of CDS. Given that the most liquid corporates in the credit default swap market number about 500, it is highly likely that each name will appear in more than one CDO tranche. Therefore, the default of one name could possibly affect several CDO tranches. Thus, we are not dealing with independent pools of assets but with combined overlapping pools of assets. We thus investigate the crucial role of the correlation parameter and provide several numerical examples pointing out the complex impact of this parameter on the risk profile and the valuation of ST CDO^sup 2^. Investors looking for trade ideas involving short or long positions in correlation could be thus interested by the results. Exhibit 1 offers a schematic representation of such instruments.
The modeling of dependence between default events is a crucial methodological step while we are concerned with the valuation and risk management of multi-name credit derivatives, like CDO^sup 2^. The common approach in the industry is based on the copula approach first introduced by Li [2000] and extended by Schonbucher and Schubert [2001], who studied the dynamics of default intensities and showed that Clayton copulas, a member of the Archimedean copula family, are related to the dependent intensities approaches of Kusuoka [1999], Davis and Lo [2001], and Giesecke [2001]. Latent factor models seem to be used for a long time to compute default events and P&L distribution (e.g., Finger [1999], Crouhy, Galai, and Mark [2000], or Schonbucher [2002]). In addition, the new Basel agreement agrees with such approaches. Interestingly enough, Frey, McNeil, and Nyfeler [2001]...