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,...

Modern regulatory capital standards, such as the Solvency II standard formula, employ a correlation based approach for risk aggregation. The so-called "square-root formula" uses correlation parameters between, for example, market risk, non-life insurance risk and default risk to determine the...