Synthetic CDO

A synthetic collateralized debt obligation creates portfolio credit exposure using credit default swaps rather than necessarily owning a pool of cash loans or bonds. Losses are allocated to tranches with different attachment and exhaustion levels. A tranche can be funded, unfunded or partly funded depending on structure. Individual default probabilities alone do not price it: dependence among defaults and recovery outcomes changes the portfolio loss distribution.

For aggregate monetary loss $L$ and monetary attachment/exhaustion levels $A<D$, this is the loss allocated to the tranche. It is zero until attachment, rises with losses between $A$ and $D$, and is capped at $D-A$. Expected tranche losses and surviving tranche notional determine protection and premium legs. For basket products whose payoff occurs at a first default, the joint default-time distribution matters as well as the final loss distribution.