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上小学 · 2023年07月24日

请问四个债券怎么比较呢?完全不明白啥意思,谁的上半年比较谁的下半年?

NO.PZ2020033002000034

问题如下:

Grapefruit Bank issued two semi-annual interest-bearing credit bonds, of which bond A matures after half a year, the coupon rate is 8.5%, the current price is $ 98, and the corresponding half-year T-bill interest rate is 4.5%. The bond B expires after one year, the coupon rate is 10%, the current price is $ 101, and the corresponding one-year T-bill rate is 5%. Assuming that their recovery rates are all 40%, and they will only default on the coupon payment date, which of the following statements is correct?

选项:

A.

The market implied risk-neutral default probability in the first half of the year is higher than that in the second half.

B.

The market implied risk-neutral default probability in the first half of the year is lower than that in the second half.

C.

The market implied risk-neutral default probability is equal in the first half and the second half.

D.

The market implied risk-neutral default probability in the first half and the second half cannot be compared.

解释:

A is correct.

考点:Spread Risk-DVCS and Credit Spread Curve

解析: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

违约概率咋还可以拆分成上半年下半年?这四个债券放一块是为了什么呢?PD是两两相同?解题完全不明白。谢谢啊

2 个答案

DD仔_品职助教 · 2023年07月25日

嗨,从没放弃的小努力你好:


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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加油吧,让我们一起遇见更好的自己!

DD仔_品职助教 · 2023年07月24日

嗨,爱思考的PZer你好:


同学你好,

因为题目描述的是发行了两个债券,都是半年付息。所以可以根据半年的spread来判断违约概率。A半年后到期,B一年后到期。

这个题是在对比0-0.5年的spread 和0.5-1年的spread的大小,因此根据题意,我们用A债券的spread来代表前半年,用bond B来代表后半年。

因为A债券的收益率算出来的其实是0-0.5年的收益率,而B债券算的是1年的收益率,所以前半年选A债券,而一年的spread可以看成是前半年spread和后半年spread的某种意义上的平均,而1年的spread是3.93%,前半年是8.255%,判断下也知道后半年的spread肯定要比8.255%要小才能和8.255%平均出3.93%这个spread。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

上小学 · 2023年07月25日

您好,谢谢,但是请问前半年和后半年的SPREAD 是怎么计算出来的呢?利用哪个条件计算的?是COUPON RATE 减去INTEREST RATE 吗?还是完全不明白怎么计算。

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