FRM Part II · FRM Exam Part II · Credit Value at Risk
A bank has 5 year cumulative default probabilities for a BB-rated obligor. The cumulative PD at 1 year is 2.0% and at 2 years is 5.0%. Assuming default can only occur once, what is the marginal (conditional) default probability in year 2, given survival through year 1?
The conditional year-2 default probability is the year-2 unconditional default probability of 3% divided by year-1 survival of 98%, which equals about 3.06%. Conditioning on survival raises it above the simple 3% difference in cumulative PDs.
- A3.00%
- B3.06%Correct
- C2.50%
- D3.47%
Explanation
Survival to year 1 is 98%; survival to year 2 is 95%. Conditional PD in year 2 = (0.98 − 0.95)/0.98 = 3.06%. The 3.00% option is the unconditional marginal PD, which fails to condition on survival.
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