高斯因子模型中贷款组合分券预期损失的快速计算：使用Hermite展开提高精度
Fast Computation of the Expected Loss of a Loan Portfolio Tranche in the Gaussian Factor Model: Using Hermite Expansions for Higher Accuracy
AI总结：
针对高斯因子模型，提出一种基于Hermite展开的快速算法，用于计算贷款组合分券的预期损失，在小规模组合上比现有方法更准确。
摘要：
我们提出了一种快速算法，用于计算高斯因子模型中的预期分券损失。我们在单因子高斯模型下，对规模从25（DJ iTraxx Australia的规模）到100（DJCDX.NA.HY的规模）的投资组合进行了测试，结果表明该算法给出了准确的结果。这里提出的算法是对\cite{PO}中算法的扩展。新算法的优点在于，对于\cite{PO}中提出的正态近似不够准确的小规模投资组合，它也能很好地工作。该算法旨在作为基于傅里叶变换的较慢方法\cite{MD}的替代方案。
英文摘要：
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}.
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