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Importance Sampling for Portfolio Credit Risk

by Paul Glasserman of Columbia University, and
Jingyi Li of Columbia University

February 2005

Abstract: Monte Carlo simulation is widely used to measure the credit risk in portfolios of loans, corporate bonds, and other instruments subject to possible default. The accurate measurement of credit risk is often a rare-event simulation problem because default probabilities are low for highly rated obligors and because risk management is particularly concerned with rare but significant losses resulting from a large number of defaults. This makes importance sampling (IS) potentially attractive. But the application of IS is complicated by the mechanisms used to model dependence between obligors, and capturing this dependence is essential to a portfolio view of credit risk. This paper provides an IS procedure for the widely used normal copula model of portfolio credit risk. The procedure has two parts: One applies IS conditional on a set of common factors affecting multiple obligors, the other applies IS to the factors themselves. The relative importance of the two parts of the procedure is determined by the strength of the dependence between obligors. We provide both theoretical and numerical support for the method.

Keywords: Monte Carlo simulation, variance reduction, importance sampling, portfolio credit risk.

Published in: Management Science, Vol. 51, No. 11, (November 2005), pp. 1643-1656.

Previously titled: Importance Sampling for a Mixed Poisson Model of Portfolio Credit Risk

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