Pricing tranches of a CDO and a CDS index: Recent advances and future research

In recent Years, the market for credit derivatives has developed rapidly with the introduction of new contracts and the standardization of trade documentation. These include credit default swaps, basket default swaps, credit default swap indexes, collateralized debt obligations, and credit default swap index tranches. Along with the introduction of new products comes the issue of how to price them. For single-name credit default swaps, there are several factor models (one-factor and two-factor models) proposed in the literature. However, for credit portfolios, much work has to be done in formulating models that fit market data. The difficulty in modeling lies in estimating the correlation risk for a portfolio of credits. In an April 16, 2004 article in the Financial Times [5], Darrell Duffie made the following comment on modeling portfolio credit risk: "Banks, insurance companies and other financial institutions managing portfolios of credit risk need an integrated model, one that reflects correlations in default and changes in market spreads. Yet no such model exists." Almost a Year later, a March 2005 publication by the Bank for International Settlements noted that while a few models have been proposed, the modeling of these correlations is "complex and not yet fully developed." [1]. In this paper, first we review three methodologies for pricing CDO tranches. They are the one-factor copula model, the structural model, and the loss process model. Then we propose how the models can be improved.