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张思琪05883 · 2022年05月24日

这里的N为什么不是0.5,1?

NO.PZ2019052801000035

问题如下:

Assume that the annualized 6-month spot rate is 5.2%, the 1-year spot rate is unknown, both spots are continuously compounded rates. A $100 face value, 1-year, 6% semiannual bond is priced at $97.83. Calculate the 1-year spot rate:

选项:

A.

7.63%

B.

8.18%

C.

9.21%

D.

10.96%

解释:

B is correct.

考点:Interest Rate

解析:

annualized 6-month spot rate表示为 Z1Z_1,1-year spot rate Z2Z_2

B=3×e[(Z1/2)×1]+103×e[(Z2/2)×2]B=3\times e^{\lbrack{(-Z_1/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack};

$97.83=3×e[(0.052/2)×1]+103×e[(Z2/2)×2]\$97.83=3\times e^{\lbrack{(-0.052/2)}\times1\rbrack}+103\times e^{\lbrack{(-Z_2/2)}\times2\rbrack};

Z2=0.081832=8.18%Z_2=0.081832=8.18\%

这里的N为什么不是0.5,1?

1 个答案

DD仔_品职助教 · 2022年05月25日

嗨,爱思考的PZer你好:


因为这里是以半年来进行计算的,利率从年化变成了半年化,N也要相对应,从多少年变成多少半年。z/2是半年化的利率。

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