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NO.PZ2018062006000064

问题如下：

Alex wants to buy a 3-year bond with the coupon rate of 5%. The coupon is paid annually. Spot rates are as follows: 1-year spot rate=4%; 2-year spot rate=4.5%; 3-year spot rate=5%.

The price of the bond is:

选项：

110.00

100.09

90.16

解释：

B is correct.

$PV = {PMT\over (1+0.04)}+{PMT\over (1+0.045)^2}+{PMT+PAR\over (1+0.05)^3} = {5\over (1+0.04)}+{5\over (1+0.045)^2} +{5+100\over (1+0.05)^3}=100.09$

PV = 100.09

考点：Pricing Bonds with Spot Rates

解析：通过未来现金流折现求和，第一年的现金流(5)用S₁ 折现，第二年的现金流(5)用S₂ 折现，第三年的现金流(100+5)用S₃ 折现，可得债券价格为100.09，故选项B正确。

如果不通过计算，coupon rate是5%，discount rate是低于等于5的，为什么price还大于100呢

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吴昊_品职助教 · 2022年04月27日

嗨，爱思考的PZer你好：

当coupon rate等于discount rate，债券价格等于面值。

当coupon rate大于discount rate，债券价格高于面值，你可以理解成分母变小，分数值反而变大了。就是下图中红框的情况，参考基础班讲义P135页。

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加油吧，让我们一起遇见更好的自己！

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NO.PZ2018062006000064 问题如下 Alex wants to buy a 3-yebonwith the coupon rate of 5%. The coupon is paiannually. Spot rates are follows: 1-yespot rate=4%; 2-yespot rate=4.5%; 3-yespot rate=5%.The priof the bonis: A.110.00 B.100.09 C.90.16 B is correct.PV=PMT(1+0.04)+PMT(1+0.045)2+PMT+PAR(1+0.05)3=5(1+0.04)+5(1+0.045)2+5+100(1+0.05)3=100.09PV = {PMT\over (1+0.04)}+{PMT\over (1+0.045)^2}+{PMT+PAR\over (1+0.05)^3} = {5\over (1+0.04)}+{5\over (1+0.045)^2} +{5+100\over (1+0.05)^3}=100.09PV=(1+0.04)PMT+(1+0.045)2PMT+(1+0.05)3PMT+PAR=(1+0.04)5+(1+0.045)25+(1+0.05)35+100=100.09PV = 100.09考点Pricing Bon with Spot Rates解析通过未来现金流折现求和，第一年的现金流(5)用S1 折现，第二年的现金流(5)用S2 折现，第三年的现金流(100+5)用S3 折现，可得债券价格为100.09，故B正确。像这样spot rate是等差数列的，能不能有什么快速选择方法？比如假设折现率都是spot rate的均值4.5%，3期，和这样算出来的价格作比较？

2023-06-10 10:56 1 · 回答

NO.PZ2018062006000064问题如下Alex wants to buy a 3-yebonwith the coupon rate of 5%. The coupon is paiannually. Spot rates are follows: 1-yespot rate=4%; 2-yespot rate=4.5%; 3-yespot rate=5%.The priof the bonis: A.110.00 B.100.09 C.90.16 B is correct.PV=PMT(1+0.04)+PMT(1+0.045)2+PMT+PAR(1+0.05)3=5(1+0.04)+5(1+0.045)2+5+100(1+0.05)3=100.09PV = {PMT\over (1+0.04)}+{PMT\over (1+0.045)^2}+{PMT+PAR\over (1+0.05)^3} = {5\over (1+0.04)}+{5\over (1+0.045)^2} +{5+100\over (1+0.05)^3}=100.09PV=(1+0.04)PMT+(1+0.045)2PMT+(1+0.05)3PMT+PAR=(1+0.04)5+(1+0.045)25+(1+0.05)35+100=100.09PV = 100.09考点Pricing Bon with Spot Rates解析通过未来现金流折现求和，第一年的现金流(5)用S1 折现，第二年的现金流(5)用S2 折现，第三年的现金流(100+5)用S3 折现，可得债券价格为100.09，故B正确。这题是三年期债券，为什么不能直接把3 yespot rate 当作I/Y，然后因为I/Y与coupon rate一样，所以债券价格等于面值。我这样的想法是哪里错了？谢谢老师。

2022-03-18 13:46 1 · 回答

请问favalue未知怎么求得是100

2019-07-13 18:29 1 · 回答

计算出错了吧？应该怎么也不会是0.09吧？

2019-04-15 10:01 2 · 回答

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