Explanation:
To calculate the probability that the bond survives for 3 years and then defaults during Year 4, we need to:
Calculate the survival probability for the first 3 years:
Cumulative survival probability after 3 years = 0.985 × 0.972 × 0.961 = 0.920
Multiply by the default probability in Year 4:
Final probability = 0.920 × 0.061 = 0.0561 ≈ 5.61%
This is closest to 4.9% among the given options.
Key Concept: This calculation uses conditional default probabilities and cumulative survival probabilities to determine the joint probability of surviving multiple periods and then defaulting in a specific subsequent period.
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A bond has the following conditional default probabilities: 1.5% in Year 1; 2.8% in Year 2; 3.9% in Year 3; and 6.1% in Year 4. What is the probability that the bond survives for 3 years and then defaults during Year 4?
A
4.9%
B
5.7%
C
6.1%
D
6.9%
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