Fast Computation of the Expected Loss of a Loan Portfolio Tranche in the Gaussian Factor Model: Using Hermite Expansions for Higher Accuracy

Abstract

We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model. We test it on portfolios ranging in size from 25 (the size of DJ iTraxx Australia) to 100 (the size of DJCDX.NA.HY) with a single factor Gaussian model and show that the algorithm gives accurate results. The algorithm proposed here is an extension of the algorithm proposed in \cite{PO}. The advantage of the new algorithm is that it works well for portfolios of smaller size for which the normal approximation proposed in \cite{PO} in not sufficiently accurate. The algorithm is intended as an alternative to the much slower Fourier transform based methods \cite{MD}.