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Grayson · 2022年09月12日

答案里面的句子不理解

NO.PZ2019011002000008

问题如下：

Bond B is a 5-year corporate bond with a fixed coupon rate of 7%. The coupon is paid annually. The bond is rated at AA.

Assume the fair value of the bond is 1098.14. The bond’s value assuming no default (VND) is 1187.22.

Li, a credit analyst in a wealth management firm, wants to know the credit spread of Bond B over a theoretical comparable-maturity government bond with the same coupon rate as this bond.

According to the information above, the credit spread is closest to:

选项：

A.

1.78%

B.

1.83%

C.

2.55%

解释：

B is correct.

考点：计算Credit spread

解析：

已知该公司债的Fair value是1098.14，并且该债券是5年期，Coupon rate为7%，根据债券定价，可以反求出其YTM:

${l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1098.14$

反求出来的YTM为4.75%。

而有题干信息The bond’s value assuming no default (VND) is 1187.22，可知利用无风险利率对该债券折现出来的价值为1187.22，该价值就等于假设的期限相同Coupon rate相同国债的价格，通过该价格反求出来的YTM就是对应假设国债的YTM：

${l}\frac{70}{(1+YTM)}+\frac{70}{(1+YTM)^2}+\frac{70}{(1+YTM)^3}+\frac{70}{(1+YTM)^4}+\frac{1070}{(1+YTM)^5}\\=1187.22$

经过计算YTM为：2.92%

则Credit spread为：4.75% - 2.92% = 1.83%

“可知利用无风险利率对该债券折现出来的价值为1187.22，该价值就等于假设的期限相同Coupon rate相同国债的价格，通过该价格反求出来的YTM就是对应假设国债的YTM” 答案中的这句话不太理解，为什么无风险利率折现出来的价值就是国债的价格？

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pzqa015 · 2022年09月13日

嗨，努力学习的PZer你好：

因为计算国债价格所用的折现率，是benchmark rate，或者说是无风险利率yb

计算公司债价格所用的折现率是yc，yc=yb+spread

----------------------------------------------
努力的时光都是限量版，加油！

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