CDO pricing with expected loss parametric interpolation

ABSTRACT This paper describes a method for pricing synthetic collateralized debt obligation transactions based on a polynomial interpolation of expected loss. This interpolation depends on a set of parameters, which can be adjusted in order to influence the price of tranchelets produced by the model. The existence of this interpolation is characterized by simple conditions on the parameters. This method overcomes the incoherence observed when using direct interpolation of base correlations. Indeed, with an interpolation of base correlations, the fair spread of a tranchelet may be locally increasing with respect to its attachment point. The polynomial interpolation of expected loss eliminates these inconsistencies. This point is illustrated by numerical comparison to other standard methods (base correlation interpolation, random factor loading and Lévy base correlation). For both iTraxx and CDX indexes, under different market regimes, the polynomial interpolation of expected loss appears to be a robust and stable method.