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FRM Part II · FRM Exam Part II · Credit Derivatives

A five-year CDS has a quoted spread of 150 bps. Assume a constant hazard rate, a recovery rate of 40%, and the credit triangle approximation. A risk manager estimates the annual risk-neutral default probability and then the five-year survival probability using continuous compounding. Which is closest to the five-year survival probability?

Hazard rate is 1.5% divided by 60%, or 2.5%. Five-year survival is exp(-0.125), about 88.2%, so the closest choice is 86.1%. Using the spread alone without dividing by loss given default would give a different, wrong figure.

  1. A68.0%
  2. B77.9%Correct
  3. C92.3%
  4. D86.1%

Explanation

Hazard rate = spread/(1-R) = 0.015/0.6 = 0.025. Survival over five years = exp(-0.025 x 5) = exp(-0.125) = 0.8825, which is about 88.2%. Checking the options: none equals that exactly, so recompute: exp(-0.125) = 0.8825. The closest option is 86.1%.

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