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Default Correlation: From Definition to Proposed Solutions

by Douglas Lucas of USB

August 11, 2004

Abstract: We define default correlation, discuss its drivers, and show why we care about it. We show pictorial representations of default probability and default correlation and derive mathematical formulas relating default correlation to default probability. We show that pairwise default correlations are not sufficient to understand the behavior of a credit risky portfolio and introduce "higher orders of default correlation." We survey the work done on historic default correlation, showing that default correlations within well-diversified portfolios vary by the ratings of the credits and also by the time period over which defaults are examined. But we also describe the major problems in measuring and even thinking about default correlation. The thorniest problem is that when looking at historical rates of default, it is impossible to distinguish default correlation from changing default probability. We compare different approaches of incorporating default correlation into portfolio credit analysis. We opine that the CSFB approach makes the most direct use of historical data and is the easier to understand.

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