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FRM Part I · FRM Exam Part I · Measuring Credit Risk

A risk analyst uses a reduced-form model with a constant hazard rate of 3% per year. What is the probability that the issuer defaults during year 2 (that is, survives year 1 but defaults before the end of year 2), using continuous time? Choose the closest value.

The year-2 default probability is about 2.87%, closest to 2.91%. It equals the survival probability to year 1 (e^-0.03) minus survival to year 2 (e^-0.06). The 5.82% option is the cumulative two-year default probability, not the marginal year-2 figure.

  1. A5.82%
  2. B2.91%Correct
  3. C6.00%
  4. D8.74%

Explanation

Survival to year 1 = e^-0.03 = 0.970446. Survival to year 2 = e^-0.06 = 0.941765. Default in year 2 = 0.970446 - 0.941765 = 0.028681, about 2.87%, closest to 2.91%? Check precisely: 0.970446 x (1 - e^-0.03) = 0.970446 x 0.029554 = 0.028681, i.e., 2.87%. Closest option is 2.91%. Cumulative two-year default is 5.82%; 6.00% is a simple sum of hazard rates; 8.74% is a three-year cumulative figure.

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