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青豆° · 2022年02月09日

关于这种题型的spot rate的time to maturity

NO.PZ2016031001000093

问题如下：

A corporate bond offers a 5% coupon rate and has exactly 3 years remaining to maturity. Interest is paid annually. The following rates are from the benchmark spot curve:

The bond is currently trading at a Z-spread of 234 basis points. The value of the bond is closest to:

选项：

A.

92.38.

B.

98.35.

C.

106.56.

解释：

A is correct.

The value of the bond is closest to 92.38. The calculation is:

$PV=\frac{PMT}{{(1+S1+Z)}^1}+\frac{PMT}{{(1+S2+Z)}^2}+\frac{PMT+FV}{{(1+S3+Z)}^3}\\=\frac5{{(1+0.0486+0.0234)}^1}+\frac5{{(1+0.0495+0.0234)}^2}+\frac{105}{{(1+0.0565+0.0234)}^3}\\=\frac5{1.0720}+\frac5{1.15111}+\frac{105}{1.25936}=4.66+4.34+83.38=92.38$

考点：bond valuation

解析：由于本题给了Z-spread，所以要在各年的Spot rate基础上再加上Z-spread，才是这只债券现金流的对应折现率。第一年现金流(5)用折现率(7.2%)折现，第二年现金流(5)用折现率(7.29%)折现，第三年现金流(5+100)用折现率(7.99%)折现，通过现金流折现求和，可得债券价格为92.38，故选项A正确。

老师你好，如果按照题目的解法，1 year 是4.86+spread；1-2 year是4.95+spread；2-3 year是5.65+spread，那这样spot rate的含义看起来就跟forward rate一样了呢？

我本来以为spot rate就是从开始到t时刻的零息利率，比如4.86就是0-1 year的rate，4.95就是0-2 year的rate，5.65就是0-3 year的rate。麻烦老师解释一下，谢谢。

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吴昊_品职助教 · 2022年02月10日

嗨，从没放弃的小努力你好：

不是的，表格中给的就是一年期、两年期和三年期的spot rate。原版书是这么给出的，我们也要习惯这样的表述。

距离到期还有一年，就是一年期的spot rate。距离到期还有两年，就是两年期的spot rate。距离到期还有三年，就是三年期的spot rate。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2016031001000093问题如下A corporate bonoffers a 5% coupon rate anhexactly 3 years remaining to maturity. Interest is paiannually. The following rates are from the benchmark spot curve:The bonis currently trang a Z-spreof 234 basis points. The value of the bonis closest to:A.92.38.B.98.35.C.106.56. A is correct.The value of the bonis closest to 92.38. The calculation is:PV=PMT(1+S1+Z)1+PMT(1+S2+Z)2+PMT+FV(1+S3+Z)3=5(1+0.0486+0.0234)1+5(1+0.0495+0.0234)2+105(1+0.0565+0.0234)3=51.0720+51.15111+1051.25936=4.66+4.34+83.38=92.38PV=\frac{PMT}{{(1+S1+Z)}^1}+\frac{PMT}{{(1+S2+Z)}^2}+\frac{PMT+FV}{{(1+S3+Z)}^3}\\=\frac5{{(1+0.0486+0.0234)}^1}+\frac5{{(1+0.0495+0.0234)}^2}+\frac{105}{{(1+0.0565+0.0234)}^3}\\=\frac5{1.0720}+\frac5{1.15111}+\frac{105}{1.25936}=4.66+4.34+83.38=92.38PV=(1+S1+Z)1PMT+(1+S2+Z)2PMT+(1+S3+Z)3PMT+FV=(1+0.0486+0.0234)15+(1+0.0495+0.0234)25+(1+0.0565+0.0234)3105=1.07205+1.151115+1.25936105=4.66+4.34+83.38=92.38考点bonvaluation解析由于本题给了Z-sprea所以要在各年的Spot rate基础上再加上Z-sprea才是这只债券现金流的对应折现率。第一年现金流(5)用折现率(7.2%)折现，第二年现金流(5)用折现率(7.29%)折现，第三年现金流(5+100)用折现率(7.99%)折现，通过现金流折现求和，可得债券价格为92.38，故A正确。两个问题1、在spot rate 加上z-sprea个知识点在哪里；2、time to maturity的意思不是距离到期日的剩余时间吗？这样表达是不是有歧义？

2023-10-04 17:17 1 · 回答

NO.PZ2016031001000093问题如下 A corporate bonoffers a 5% coupon rate anhexactly 3 years remaining to maturity. Interest is paiannually. The following rates are from the benchmark spot curve:The bonis currently trang a Z-spreof 234 basis points. The value of the bonis closest to:A.92.38.B.98.35.C.106.56. A is correct.The value of the bonis closest to 92.38. The calculation is:PV=PMT(1+S1+Z)1+PMT(1+S2+Z)2+PMT+FV(1+S3+Z)3=5(1+0.0486+0.0234)1+5(1+0.0495+0.0234)2+105(1+0.0565+0.0234)3=51.0720+51.15111+1051.25936=4.66+4.34+83.38=92.38PV=\frac{PMT}{{(1+S1+Z)}^1}+\frac{PMT}{{(1+S2+Z)}^2}+\frac{PMT+FV}{{(1+S3+Z)}^3}\\=\frac5{{(1+0.0486+0.0234)}^1}+\frac5{{(1+0.0495+0.0234)}^2}+\frac{105}{{(1+0.0565+0.0234)}^3}\\=\frac5{1.0720}+\frac5{1.15111}+\frac{105}{1.25936}=4.66+4.34+83.38=92.38PV=(1+S1+Z)1PMT+(1+S2+Z)2PMT+(1+S3+Z)3PMT+FV=(1+0.0486+0.0234)15+(1+0.0495+0.0234)25+(1+0.0565+0.0234)3105=1.07205+1.151115+1.25936105=4.66+4.34+83.38=92.38考点bonvaluation解析由于本题给了Z-sprea所以要在各年的Spot rate基础上再加上Z-sprea才是这只债券现金流的对应折现率。第一年现金流(5)用折现率(7.2%)折现，第二年现金流(5)用折现率(7.29%)折现，第三年现金流(5+100)用折现率(7.99%)折现，通过现金流折现求和，可得债券价格为92.38，故A正确。直接用三年期的Sport rate 为benchmark所以求出I/Y=5.65+234bps =7.99再用计算器算出PV=92.29。也是closetob答案A

2023-06-22 08:44 1 · 回答

NO.PZ2016031001000093 问题如下 A corporate bonoffers a 5% coupon rate anhexactly 3 years remaining to maturity. Interest is paiannually. The following rates are from the benchmark spot curve:The bonis currently trang a Z-spreof 234 basis points. The value of the bonis closest to: A.92.38. B.98.35. C.106.56. A is correct.The value of the bonis closest to 92.38. The calculation is:PV=PMT(1+S1+Z)1+PMT(1+S2+Z)2+PMT+FV(1+S3+Z)3=5(1+0.0486+0.0234)1+5(1+0.0495+0.0234)2+105(1+0.0565+0.0234)3=51.0720+51.15111+1051.25936=4.66+4.34+83.38=92.38PV=\frac{PMT}{{(1+S1+Z)}^1}+\frac{PMT}{{(1+S2+Z)}^2}+\frac{PMT+FV}{{(1+S3+Z)}^3}\\=\frac5{{(1+0.0486+0.0234)}^1}+\frac5{{(1+0.0495+0.0234)}^2}+\frac{105}{{(1+0.0565+0.0234)}^3}\\=\frac5{1.0720}+\frac5{1.15111}+\frac{105}{1.25936}=4.66+4.34+83.38=92.38PV=(1+S1+Z)1PMT+(1+S2+Z)2PMT+(1+S3+Z)3PMT+FV=(1+0.0486+0.0234)15+(1+0.0495+0.0234)25+(1+0.0565+0.0234)3105=1.07205+1.151115+1.25936105=4.66+4.34+83.38=92.38考点bonvaluation解析由于本题给了Z-sprea所以要在各年的Spot rate基础上再加上Z-sprea才是这只债券现金流的对应折现率。第一年现金流(5)用折现率(7.2%)折现，第二年现金流(5)用折现率(7.29%)折现，第三年现金流(5+100)用折现率(7.99%)折现，通过现金流折现求和，可得债券价格为92.38，故A正确。老师好，请问这里的SPOT RATE 与 FORWARRATE有什么区别，谢谢

2023-02-20 05:30 1 · 回答

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2022-12-02 09:32 1 · 回答

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2022-10-18 19:58 1 · 回答