runruncat · 2023年06月10日
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：
A.110.00
B.100.09
C.90.16
解释：
B is correct.
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。
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？
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。 如果不通过计算，coupon rate是5%，scount rate是低于等于5的，为什么price还大于100呢
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。
请问favalue未知 怎么求得是100
计算出错了吧？应该怎么也不会是0.09吧？
