Monday, 12 November 2007

Level 3 and default correlation

Suppose you take a collection of assets of known price and put them into an SPV. The SPV issues tranched debt. Obviously the sum of the values of the tranches equals the sum of the values of the original assets (unless there is some external credit enhancement for the SPV which adds value, or some other external influence).

Clearly too in a conventional tranching structure the senior tranche bears the least default risk and the junior tranche the most. But what is the fair value of each silo individually?
This is the problem many banks are facing at the moment. They have either retained tranches in their own CDOs or purchased tranches in other people's, and these securities have not traded for some time. Therefore level 1 (mark to an observable market price) valuation is impossible. The assets have to be valued, though, so they have to do something, albeit in level 3.

The basic modeling problem is to assign value between tranches. This assignment depends on something that is popularly known as default correlation, but should properly be called default comovement: if the occurrence of one default in the CDO assets makes another much more likely, then the senior tranche is less valuable. If one default is more or less unrelated to another, then the senior is safer and hence more valuable.

Default comovement is idiosyncratic. There is no reason to believe it will be the same between one pool of mortgages and another, let along between one diverse pool of ABS and another. Some limited information on it in particular cases can be inferred from the prices of the few liquid securities - the iTraxx tranches and the ABX, for instance - but there is no compelling reason to believe this carries over to other asset pools. This means that more or less any CDO tranche at the moment is a level 3 asset and any valuation necessarily has a measure of model risk and/or model parameter risk.

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