Large deviations in multifactor portfolio credit risk

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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.
Publisher
BLACKWELL PUBLISHING
Issue Date
2007-07
Language
English
Article Type
Article
Citation

MATHEMATICAL FINANCE, v.17, no.3, pp.345 - 379

ISSN
0960-1627
DOI
10.1111/j.1467-9965.2006.00307.x
URI
http://hdl.handle.net/10203/24688
Appears in Collection
MA-Journal Papers(저널논문)
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