The hybrid saddlepoint method for credit portfolios

Most real-world portfolios are not homogeneous in exposure or probability of default yet many practitioners use analytic portfolio models that explicitly or implicitly assume homogeneity. This can lead to significant errors when estimating the shape of the loss distribution, calculating quantities such as the value-at-risk or valuing tranches of structured products. One such approach is the standard saddlepoint approximation derived by Daniels (1954) to estimate the density of the mean of severa