FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk
A bank buys a full guarantee on a USD 100 million loan to Borrower X (probability of default 4%) from Guarantor G (probability of default 2%). Assume default of X and G are independent, and loss given default is 100% for simplicity. What is the probability the bank suffers a loss on the loan?
The probability of loss is 0.08%. With a full guarantee and independent defaults, the bank suffers a loss only when both borrower and guarantor default, so the joint probability is 4% times 2%, which equals 0.08%.
- A0.08%Correct
- B2.00%
- C4.00%
- D6.00%
Explanation
The bank loses only if both the borrower and guarantor default. With independence: 0.04 x 0.02 = 0.0008 = 0.08%. Adding probabilities (6%) ignores that the guarantee only fails if both default; 4% ignores the guarantee.
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