郭大路 · 2020年02月04日
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:
我的计算方式是否也是对的。答案说92.9.
先通过Spot rate 算出 benchmark YTM, 5.61%. 然后+上Z，得出corporate bond，ytm是7.95%。然后用计算器算出来。
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？
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
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
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。 有没有情况是用spot rate-z sprea折现的呢？
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。 为啥按%计算结果哪怕加上括号都不对？计算器算的时候只能百分数化小数吗？
