In this article, we present an accurate analytical approximation for a joint distribution function of loss of two overlapping credit portfolios using the multidimensional saddlepoint method. The same method is applied to the tail probability of loss from two tranches and to CDO-squared. Numerical examples show that the default correlations effectively destroy non-normal tails, making the conditional normal approximation viable in many practical cases.

Authors: Timur Misirpashaev, and Alexander Antonov