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Catherine · 2023年08月04日

spread公式

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

spread=PD✖️RR在讲义哪里讲的

Catherine · 2023年08月04日

知道公式了,想问下怎么看出来这个题用这个知识点呢

1 个答案

品职答疑小助手雍 · 2023年08月04日

同学你好,我个人的思路哈,看到选项里都在问的是The market implied risk-neutral default probability在0-0.5年和0.5-1年的对比,就可以和一级里面已知spot rate反求forward rate的提类比了,思路是一样的。

两个债券跟无风险债比较的差异就是spread的,而本题的结论就需要靠前后两个半年的spread对比得出。

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