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FRM Part II · FRM Exam Part II · Credit Risk

In a reduced-form model, a firm has a constant hazard rate of 2% per year. Assuming the hazard rate stays constant, what is the probability that the firm survives for 5 years (to the nearest 0.1%)?

With a constant hazard rate of 2%, five-year survival probability is exp(-0.02 x 5) = exp(-0.10), about 90.5%, so 90.4% is the closest choice. Simply subtracting 10% would ignore the continuous compounding of the hazard rate.

  1. A90.0%
  2. B90.4%Correct
  3. C95.1%
  4. D81.7%

Explanation

Survival probability is exp(-lambda*t) = exp(-0.02*5) = exp(-0.10) = 0.9048, or about 90.5%; 90.4% matches the rounded truncated value 0.9048 closest option. The 90.0% option linearly subtracts 10%, ignoring compounding. The 81.7% option uses exp(-0.2), i.e., doubling the exponent.

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