Approximating Independent Loss Distributions with an Adjusted Binomial Distribution

We present a heuristic algorithm which accurately and quickly approximates loss distributions for portfolios of independent credits. Such an algorithm 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 CDO with homogeneous losses the percentage spread error is below 0.06% across a broad range of portfolio default correlations and credit qualities. Across the range of inhomogeneous loss portfolios we tested, the error in the spread was always less than 1.5bp. For homogeneous loss portfolios the computation time is reduced by a factor of around 10, and for a typical inhomogeneous loss portfolio it is reduced by a factor of around 60 when compared to the fastest exact approach. We argue that this algorithm is a fast and accurate alternative to the exact recursion approach