Approximating independent loss distributions with an adjusted binomial distribution

ABSTRACT A heuristic algorithm that accurately and quickly approximates loss distributions for portfolios of independent credits is introduced in this paper. An algorithm such as this can be used in the implementation of conditionally independent portfolio default models. The algorithm can handle both homogeneous and inhomogeneous loss portfolios and is based on a simple adjustment of the binomial distribution. When used to price a standard single-tranche collateralized debt obligation with homogeneous losses, the percentage error in the tranche breakeven spread is below 0.06% across a broad range of portfolio default correlations and credit qualities. Across the range of inhomogeneous loss portfolios that we tested, the error in the tranche spread was always less than 1.5 basis points. Compared with the fastest exact approach, for homogeneous loss portfolios the computational time is reduced by a factor of around ten, and, for a typical inhomogeneous loss portfolio, it is reduced by a factor of around sixty.We argue that this algorithm is a fast and accurate alternative to the exact recursion approach.