Large Correlation Structures in Pools of Defaults: A Large Deviations Analysis

Abstract

Investment-grade tranches of pools of assets by design suffer losses only rarely. The rarity of the events, or equivalently, the size of the tail, depend crucially upon the correlation between the assets. We here study the asymptotics of a model for credit assets, where correlations are due to a two-stage hierarchy of randomness. We find that this gives a richer structure of possibilities than are present in a one-stage model of many idiosyncratic random variables and a small number of systemic random variables. Our calculations take advantage of the theory of large deviations.

Keywords: correlation, structured finance, large deviations

JEL Classification: C63