Synthetic CDO Squared Pricing Methodologies

We propose two different methodologies for the pricing of CDO squared and by extension for the risk management of funds of CDO tranches. The first methodology is based on a drill-down approach whereas the second one is based on a "correlation of correlation" approach. Our purpose is to be consistent with the inner CDOs characteristics because of several issues that need to be addressed. The correlation "skew" of each underlying inner CDO must be reproduced. The outer correlation, the correlation of joint loss distributions, among the losses of the inner CDOs must be considered. The outer correlation, which can be interpreted as a global correlation "skew", depends on the overlapping characteristics, the spread level and recovery rate assumptions for each credit in the portfolio, and the correlation structure among the credits. We demonstrate that using these approaches we can obtain a very good proxy for complex structures prices in the correlation market. Nevertheless we have to mention some theoretical drawbacks. The drill-down methodology is consistent with the outer correlation but assumes that prices of the inner tranches are driven by the same market correlation "skew". The "correlation of correlation" approach is consistent with inner tranches pricing but not with the outer correlation. We also illustrate the fact that the pricing should be very sensitive to the level of outer correlation when we use the "correlation of correlation" methodology. We demonstrate that using these two methodologies we can now efficiently price CDO squared and risk manage funds of CDO tranches.