Severe Loss Probabilities in Portfolio Credit Risk Models

Abstract

We derive explicit sharp bounds on the distribution of the number of defaults from a pool of obligors with common probability of default and default correlation. These bounds are extremely wide, implying that default probabilities and default correlations only very loosely determine estimates of severe portfolio losses. Our results quantify and thereby reinforce Gordy's (2002) statement that "Capital decisions . . . depend on higher moments".

Keywords: Portfolio, credit, risk, models,default, loss, probabilities, severe

JEL Classification: G31, C16, G11