The marginal probability of default for years one and two is 0.5% and1.1 %,respectively.

Ifthe cumulative probability of default for the 3-year period is 4.45%, the marginal probability of default for year three is closest to:

A. 2.8%

B. 3.2%

C. 2.9%

D. 2.7%

Answer：C

The cumulative probability of default is equal to one minus the probability of surviving to the end ofthe period without default:

C3 =1 一(1-Pl)(1 一 P2 )(1 一 P3)0.0445 = 1-(1-0.005)(1-0.01 ~)(1-P3)*P3 =2.9%

本题翻译为：

第一年和第二年的边际违约概率分别为0.5%和1.1%。

如果三年期累计违约概率为4.45%，那么第三年违约的边际概率最接近于：

A. 2.8%

B. 3.2%

C. 2.9%

D. 2.7%

答案：C

累计违约概率等于1减去未违约期间存活到期末的概率：

C3 = 1一(1-P1)(1一P2)(1一P3)0.0445 = 1-(1-0.005)(1-0.01-)(1-P3)* P3 = 2.9%

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