On Some Inconsistencies in Modelling Credit Portfolio Products

The survival probability term structure has become the main concept in modeling credit risk for pricing, risk management, and investment decisions. The Kth-to-default contract is not only a relatively liquid credit risk instrument but also a vehicle that credit rating agencies employ to determine the rating of more esoteric credit risky positions. In this paper, we point out some subtleties in credit risk modeling of default baskets and also identify some potential bias in the pricing formula of the Kth-to-default contract. The numerical examples suggest that this bias increases with the correlation. The results in this paper emphasize the important role of conditioning the information regarding arrival of default.