Abstract: Evaluating default correlations and the probabilities of multiple defaults is an important task in credit analysis and risk management, but it has never been an easy one because default correlations cannot be measured directly. This paper provides, for the first time, an analytical formula for calculating default correlations based on a first-passage-time model that can be easily implemented and conveniently used in a variety of financial applications. This paper also provides a theoretical justification for many empirical results found in the literature and increases our understanding of the important features of default correlations.

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