Approximating Correlated Defaults

Abstract

In the recent financial crisis, improperly modeled default correlations caused multi-billion-dollar losses. We propose parsimonious statistical approximations for correlated defaults which follow from an intensity-based risk-factor model and allow consistent parameter estimation, even if another default model is used. The parameters imply an approximating portfolio of independent, identical-credit loans and jointly characterize the default-relative diversification and average credit quality. The approach improves upon similar methods by allowing for fatter tails as well as loans differing in size and credit quality. Some guidance is also given on structuring CDOs to have credit-ratings that are robust to crises. An example shows how to estimate the approximating portfolio.

Keywords: default-approximating portfolio, diversity score, default-relative diversification, robust CDO structuring, gamma Edgeworth expansion

JEL Classification: G13, G12, C16, G33