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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

In a one-factor Gaussian copula with correlation rho = 0.25, a firm has a 5-year cumulative default probability of 2.28%, so N^-1(0.0228) = -2.00. Conditional on the common factor M = -1.00, what is the conditional default probability, N[(-2.00 - sqrt(0.25)*(-1.00))/sqrt(0.75)]? Use N(-1.73)=0.0418, N(-1.50)=0.0668, N(-2.00)=0.0228.

The conditional default probability is 4.18%. The threshold -2.00 shifted by 0.5 gives -1.50, divided by sqrt(0.75)=0.866 gives -1.73, and N(-1.73)=4.18%. Omitting the division by 0.866 yields 6.68%, which is wrong.

  1. A2.28%
  2. B4.18%Correct
  3. C6.68%
  4. D1.50%

Explanation

Numerator: -2.00 - 0.5*(-1) = -1.50. Denominator: sqrt(0.75)=0.866. Ratio = -1.732, so N(-1.73)=0.0418 = 4.18%. Using 0.0668 comes from forgetting to divide by sqrt(1-rho). Check: the stressed factor should raise PD above 2.28%, which holds.

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