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小小悟空yu · 2021年11月16日

问一道题:NO.PZ2020033002000034 [ FRM II ]

问题如下图:

我的解题思路哪里错了,coupon应该如何考虑,正确的解题思路应该是什么啊

选项:

A.

B.

C.

D.

解释:

1 个答案

DD仔_品职助教 · 2021年11月16日

嗨,努力学习的PZer你好:


同学你这个题不能这么考虑,因为针对这个债券,他的现金流是半年就有一次,而PD是年化的概念,所以你在计算的时候,针对A债券,他半年就到期,那么PD也应该是半年的。B债券,第一笔现金流是半年的,PD也是半年的,而到期有coupon和本金,此时是一年PD就考虑1年的即可。

这种有coupon的,并且是半年就有一次coupon的债券,不建议同学用这种求expected value的方法来计算,因为麻烦的很,容易出错,这种题型,建议同学直接用简化的近似的公式:YTM-rf=spread=risk-neutral PD*LGD=risk-neutral PD*(1-RR)

就像解析里写的,对于bondA,通过金融计算器:PV=-98 FV=100 PMT=4.25 N=1 CPT I/Y=6.3776 年化YTM=12.76%

spread=YTM-rf=12.76%-4.5%=8.255%

债券B:PV=-101 FV=100 PMT=5 N=2 CPT I/Y=4.466% 年化YTM=8.93%

spread=YTM-rf=8.93%-5%=3.93%

根据题目已知RR=40%,那么spread=PD*RR,谁的spread大,PD肯定就大,A这个半年期bond的PD大于B这个一年期的bond,那么前半年的PD也就肯定大于后半年的PD

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