Portfolio Credit Derivatives Top Down Dependence Diagnostics via Majorization

Abstract

We provide a novel methodology for precise diagnostics of the dependence in portfolio credit derivatives under a top-down setting. The latter framework poses a conceptual challenge since no a priori copula is assumed and it can be only implied. Doing this can help not only to have a better understanding and precisely quantify the effects that arise, but also can be of significant practical value to the financial industry in pricing and risk management. For the purpose we use powerful but not so popular techniques based on majorization. The tranche structure gives a direct access to the dependence structure of the portfolio. We focus on its boundary cases and see how they are related to the majorization.

Keywords: CDO, Lorenz curve, majorization, dependence, copula

JEL Classification: G13