Large Deviations in Multifactor Portfolio Credit Risk

35 Pages Posted: 28 Jun 2007

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Wanmo Kang

Korea Advanced Institute of Science and Technology (KAIST) - Department of Mathematical Science

Perwez Shahabuddin

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Abstract

The measurement of portfolio credit risk focuses on rare but significant large-loss events. This paper investigates rare event asymptotics for the loss distribution in the widely used Gaussian copula model of portfolio credit risk. We establish logarithmic limits for the tail of the loss distribution in two limiting regimes. The first limit examines the tail of the loss distribution at increasingly high loss thresholds; the second limiting regime is based on letting the individual loss probabilities decrease toward zero. Both limits are also based on letting the size of the portfolio increase. Our analysis reveals a qualitative distinction between the two cases: in the rare-default regime, the tail of the loss distribution decreases exponentially, but in the large-threshold regime the decay is consistent with a power law. This indicates that the dependence between defaults imposed by the Gaussian copula is qualitatively different for portfolios of high-quality and lower-quality credits.

Suggested Citation

Glasserman, Paul and Kang, Wanmo and Shahabuddin, Perwez, Large Deviations in Multifactor Portfolio Credit Risk. Mathematical Finance, Vol. 17, No. 3, pp. 345-379, July 2007, Available at SSRN: https://ssrn.com/abstract=997163 or http://dx.doi.org/10.1111/j.1467-9965.2006.00307.x

Paul Glasserman

Columbia Business School ( email )

3022 Broadway
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New York, NY 10027
United States
212-854-4102 (Phone)
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Wanmo Kang (Contact Author)

Korea Advanced Institute of Science and Technology (KAIST) - Department of Mathematical Science ( email )

373-1 Kusong-dong
Yuson-gu
Taejon 305-701, 130-722
Korea, Republic of (South Korea)

Perwez Shahabuddin

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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