FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment
Hazard rates for a borrower are 2% in year 1, 3% in year 2 and 5% in year 3 (piecewise constant, continuously compounded). What is the approximate cumulative probability of default by the end of year 3?
Add the piecewise hazard rates to get an integrated hazard of 0.10, so survival is exp(-0.10), about 90.5%. Cumulative default probability by year 3 is therefore about 9.5%, not the simple sum of 10%.
- A10.0%
- B9.5%Correct
- C7.0%
- D90.5%
Explanation
Integrated hazard = 0.02+0.03+0.05 = 0.10. Survival = exp(-0.10) = 0.9048, so cumulative default = 1 − 0.9048 ≈ 9.5%. Summing hazards to 10.0% overstates default, 7.0% ignores year 3's rate, and 90.5% is survival.
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