Default probabilities and default correlations
Starting from the Merton framework for firm defaults, we provide the analytics and robustness of the relationship between default correlations. We show that loans with higher default probabilities will not only have higher variances but also higher correlations between loans. As a consequence, portfolio standard deviation 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 on 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.
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