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Using Hermite Expansions for Fast and Arbitrarily Accurate Computation of the Expected Loss of a Loan Portfolio Tranche in the Gaussian Factor Model

by Pavel Okunev of LBNL & the University of California, Berkeley

June 19, 2005

Abstract: We propose a fast algorithm for computing the expected tranche loss in the Gaussian factor model with arbitrary accuracy using Hermite expansions. No assumptions about homogeneity of the portfolio are made. The algorithm is a generalization of the algorithm proposed in Okunev (2005). The advantage of the new algorithm is that it allows us to achieve higher accuracy in almost the same computational time. It is intended as an alternative to the much slower Fourier transform based methods.

Keywords: CDO, credit portfolio, correlation, Gaussian factor model.

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