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RyanR · 2023年04月21日

答案的描述是什么意思?

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:由bondA可以得出:98=\frac{104.25}{1+{\displaystyle\frac y2}},解出半年期bond收益率y=12.755%,那么半年期的spread就是12.755%-4.5%=8.255%。

同理得到债券B:一年期bond的收益率y=8.93%,那么一年期的spread就是8.93%-5%=3.93%。当recovery rate是一样的时候,那前半年的违约概率肯定是高于后半年的。

算法都会,结合答案的描述,没有理解这个情景。

发行了两个债券,都是半年付息。A半年后到期,B一年后到期。因为后半年只剩bondB了,所以spread就是Bond B的?算出来的BondA的spread为啥可以当作前半年的spread,




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已采纳答案

pzqa27 · 2023年04月23日

嗨,努力学习的PZer你好:


A债券是个半年的债券,B债券是个1年的债券,因此A算出的spread 代表是前半年的spread,B债券算出的spread代表是1年的,不是代表后半年,后半年是推测推出来的

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pzqa27 · 2023年04月21日

嗨,努力学习的PZer你好:


发行了两个债券,都是半年付息。A半年后到期,B一年后到期。因为后半年只剩bondB了,所以spread就是Bond B的?

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。

另外解析可没说后半年只剩bondB了,所以spread就是Bond B的,解析写的是“一年期的spread就是8.93%-5%=3.93%。当recovery rate是一样的时候,那前半年的违约概率肯定是高于后半年的。”


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RyanR · 2023年04月23日

为啥是用A债券的spread来代表前半年,B债券的spread代表后半年呢,这个地方没有搞懂

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