Implied Correlation in CDO Tranches : A Paradigm to be Handled with Care

We illustrate the two main types of implied correlation one may obtain from market CDO tranche spreads. Compound correlation is more consistent at single tranche level but for some market CDO tranche spreads cannot be implied. Base correlation is less consistent but more flexible and can be implied for a much wider set of CDO tranche market spreads. Furthermore, base correlation is more easily interpolated and leads to the possibility to price non-standard detachments. Even so, base correlation may lead to negative expected tranche losses, thus violating basic no-arbitrage conditions. We illustrate these features with numerical examples