Suppose that the cumulative probability of a company defaulting by years one, two, three and four are 3%, 6.5%, 10%, and 14.5%, respectively. What is the probability of default in the fourth year conditional on no earlier default?
A. 4.5%
B. 5.0%
C. 5.5%
D. 6.0%
B
The unconditional PD for the fourth year is 14.5% minus 10% or 4.5%. The probability of no earlier default is 90%. The PD conditional on no earlier default is therefore 0.045/0.9=0.05 or 5%
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