Default Probabilities and Default Correlations
by Ulrich Erlenmaier of the University of Heidelberg, and
Abstract: Starting from the Merton framework for firm defaults, we provide the analytics and robustness of the relationship between default probabilities and default correlations. We show that loans with higher default probabilities will not only have higher variances but also higher correlations with other loans. As a consequence, portfolio standard deviations can increase substantially when loan default probabilities rise. This result has two important implications. First, relative prices of loans with different default probabilities should reflect the differential impact of portfolio standard deviation. Second, the standard deviation of loan portfolios and of default rates, as well as the required economic capital will vary significantly over the business cycle.
Keywords: Credit portfolio management, Default correlations, Pricing of loans, Macroeconomic risk, Credit risk models.