glasserman1 - Vol 51 No 11 November 2005 pp 16431656 issn...

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MANAGEMENT SCIENCE Vol. 51, No. 11, November 2005, pp. 1643–1656 issn 0025-1909 ± eissn 1526-5501 ± 05 ± 5111 ± 1643 inf orms ® doi 10.1287/mnsc.1050.0415 © 2005 INFORMS Importance Sampling for Portfolio Credit Risk Paul Glasserman, Jingyi Li Columbia Business School, Columbia University, New York, New York 10027 {[email protected], [email protected]} M onte 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 signi±cant 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. Key words : Monte Carlo simulation; variance reduction; importance sampling; portfolio credit risk History : Accepted by Wallace J. Hopp, stochastic models and simulation; received January 19, 2004. This paper was with the authors 1 month for 3 revisions. 1. Introduction Developments in bank supervision and in markets for transferring and trading credit risk have led the ±nancial industry to develop new tools to measure and manage this risk. An important feature of mod- ern credit risk management is that it takes a portfo- lio view, meaning that it tries to capture the effect of dependence across sources of credit risk to which a bank or other ±nancial institution is exposed. Captur- ing dependence adds complexity both to the models used and to the computational methods required to calculate outputs of a model. Monte Carlo simulation is among the most widely used computational tools in risk management. As in other application areas, it has the advantage of being very general and the disadvantage of being rather slow. This motivates research on methods to accel- erate simulation through variance reduction. Two features of the credit risk setting pose a particu- lar challenge: (i) it requires accurate estimation of low-probability events of large losses; (ii) the depen- dence mechanisms commonly used in modeling port- folio credit risk do not immediately lend themselves to rare-event simulation techniques used in other settings.
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glasserman1 - Vol 51 No 11 November 2005 pp 16431656 issn...

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