Implied Expected Tranched Loss Surface from CDO Data

Abstract

We explain how the payoffs of credit indices and tranches are valued in terms of expected tranched losses (ETL). ETL are natural quantities to imply from market data. No-arbitrage constraints on ETL's as attachment points and maturities change are introduced briefy. As an alternative to the temporally inconsistent notion of implied correlation we consider the ETL surface, built directly from market quotes given minimal interpolation assumptions. We check that the kind of interpolation does not interfere excessively. Instruments bid/asks enter our analysis, contrary to Walker's (2006) earlier work on the ETL implied surface. By doing so we find less and very few violations of the no-arbitrage conditions. The ETL implied surface can be used to value tranches with nonstandard attachments and maturities as an alternative to implied correlation.

Keywords: expected tranche loss, loss surface, implied correlation, CDO, tranches, interpolation

JEL Classification: G13