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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

A trader uses a constant hazard rate implied from a 3-year CDS spread of 180 basis points with a 40% recovery rate (hazard = spread / (1 - R) = 3.00%). What is the approximate risk-neutral probability that the reference entity defaults within the 3 years, using continuous compounding?

The cumulative default probability is about 8.61%. With a constant 3% hazard rate, survival over three years is exp(-0.09), about 91.39%, so default probability is one minus that. Simply multiplying 3% by three overstates it, and 91.39% is survival.

  1. A1 - exp(-0.09) = 8.61%Correct
  2. B9.00%
  3. C1 - exp(-0.03) = 2.96%
  4. Dexp(-0.09) = 91.39%

Explanation

With a constant hazard rate of 3%, cumulative default probability over 3 years is 1 - exp(-0.03 x 3) = 1 - exp(-0.09) = 1 - 0.9139 = 8.61%. Simply multiplying by 3 ignores compounding of survival (9.00%), and 91.39% is the survival probability, not the default probability.

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