1.         Assume the marginal monthly default rates (conditional on no previous default) for a firm are 1% each month during the first year and 3% each month during the second year. What is the marginal probability of defaulting over the second year, conditional on not having defaulted the first year?

A. The question cannot be answered with the information given

B. 40.9%

C. 36.0%

D. 30.6%

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Correct answer is D

D is obtained by first calculating cumulative probabilities of default, and then applying Bayes' theorem.

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Answers B and C are obtained as a result of wrong calculations:

(b) 

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(c) 

[此贴子已经被作者于2009-6-13 10:22:00编辑过]

the explanation is too complicated.

since the result is marginal probability of default,we donot need to know the survival probability at the end of first year.

1-(1-3%)^12=30.6%

the result must be less than 36% (3%*12),there is only one answer less than 36%.