Approximating correlated defaults

Modeling defaults is critical to risk management as well as pricing debt portfolios and portfolio derivatives. In the recent financial crisis, multi-billion-dollar losses resulted from correlated defaults that were improperly modeled. This paper proposes statistical approximations which are more general than those used previously, follow from an intensity-based risk-factor model, and allow consistent parameter esti- mation. The parameters imply an approximating portfolio of independent, identical-credit loans and characterize both average credit quality and default-relative diversification (aka the “diversity score”). Unlike previous approaches, these metrics are derived jointly from theory. The approach addresses weaknesses in the typical diversity score-based methods by allowing for fatter tails as well as loans differing in size and credit quality. The approximations may also be used to model complete portfolio default and help set capital adequacy requirements. An example shows how to estimate the approximating portfolio.