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FRM Part II · FRM Exam Part II · Credit Risk

In a one-factor Gaussian copula (Vasicek) model, a large homogeneous portfolio has a one-year PD of 2% and asset correlation rho = 0.20. The 99.9% standard normal quantile is 3.090 and N^-1(0.02) = -2.054. The worst-case default rate at 99.9% is N[(N^-1(PD) + sqrt(rho) x 3.090)/sqrt(1 - rho)]. Which value is closest to this rate?

The worst-case default rate is about 22.6%, closest to 25%. Compute sqrt(0.2) x 3.090 = 1.382, add N^-1(2%) = -2.054 to get -0.672, divide by sqrt(0.8) = 0.894 to get -0.751, and N(-0.751) is roughly 0.227. This far exceeds the 2% unconditional PD.

  1. AAbout 2.0%
  2. BAbout 8.9%
  3. CAbout 14.0%Correct
  4. DAbout 25.0%

Explanation

sqrt(0.2) = 0.4472; 0.4472 x 3.090 = 1.382. Numerator = -2.054 + 1.382 = -0.672. sqrt(0.8) = 0.8944, so the argument = -0.751. N(-0.751) is about 0.226... recompute: N(-0.75) = 0.2266. Hence the rate is about 22.6%, closest to 25.0%.

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