A multifactor bottom-up model for pricing credit derivatives

ABSTRACT In this paper we continue the study of the stress event model, a simple and intuitive dynamic model for credit risky portfolios, proposed by Duffie and Singleton. The model is a bottom-up version of the multifactor portfolio credit model proposed by Longstaff and Rajan. By a novel identification of independence conditions, we are able to decompose the loss distribution of a credit risky portfolio into a series expansion which not only provides a clear picture of the characteristics of the loss distribution but also suggests a fast and accurate approximation for it. Our approach has three important features: it is able to match standard credit default swap (CDS) index tranche prices and the underlying CDS spreads; its computational speed is very fast, comparable to that of the Gaussian copula model; and the computational cost for additional factors is mild, allowing for more flexibility for calibrations and opening up the possibility of studying multifactor default dependence of a portfolio via a bottom-up approach. We demonstrate the tractability and efficiency of our approach by calibrating a three-sector model to investment-grade CDS index tranches.