问一道题：NO.PZ2016082406000020

The marginal default probabilities for an A-rated issue are, respectively, for years 1, 2, and 3: 0.300%, 0.450%, and 0.550%. Assume that defaults, if they take place, happen only at the end of the year. Calculate the cumulative default rate at the end of each of the next three years.

选项：

0.300%, 0.750%, 1.300%

0.300%, 0.150%, 0.250%

0.300%, 0.749%, 1.295%

0.300%, 0.449%, 0.548%

解释：

ANSWER: C

The default rate to the end of year 2 is the survival rate for year 1 times the year 2 default rate, ${(1-d_1)}d_2={(1-0.003)}0.0045=0.449\%$. Hence the year 2 cumulative default rate is 0.300 + 0.449 = 0.749%. The default rate to the end of year 3 is ${(1-d_1)}{(1-d_2)}d_3={(1-0.003)}{(1-0.0045)}0.0055=0.546\%$. Hence the year 3 cumulative default rate is 0.749 + 0.546 = 1.295%.

老师题目里面给的MPD，MPD2=（1- 第一年不违约的概率）*第二年违约的概率【单独的看第二年违约的概率PD】

但是看答案貌似是，吧MPD2直接当成了d2来用了。。