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格日乐图 · 2025年04月21日

固定利率为什么不用已知的固定利率4%算呢?

NO.PZ2019052801000049

问题如下:

A bank entered into a swap with two years to maturity as a floating rate payer. The fixed rate is 4%, with annal payments. The notional priciple is $5,000,000. The spot interest rates are as follows: one year, 3.5%; two years, 4.5%. Today is the reset day, the current value of the swap is closest to:

选项:


A.

$54,437.

B.

$-54,437.

C.

-$30,125.

D.

$30,125.

解释:

B is correct.

考点:利率互换估值.

解析:

支浮动的一方可以看作一个浮动利率债券,浮动利率债券在reset day 价值回归面值。

收固定的一方可以看作一个固定利率债券,

Bfix  =0.04e0.035+1.04e0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113

lV=(0.9891131)×5,000,000=54,437{l}\\V=(0.989113-1)\times5,000,000=-54,437

如题。固定利率为什么不用已知的固定利率4%算呢?

1 个答案

李坏_品职助教 · 2025年04月21日

嗨,爱思考的PZer你好:


这个固定利率的一方就是用的4%来计算利息的啊。


固定利率的价值是Bfix,Bfix = 4% * e^(-0.035) + 1.04*e(-0.045*2)= 0.989113. 这个算的是假设本金为1美元,那么固定利率部分的价值为0.989113美元。注意固定利率部分后续的现金流是有一笔利息,就是4%, 然后还有一笔是本金1美元+利息4%,所以第二笔现金流是1.04.


而浮动利率部分的价值就等于本金1美元。最后用固定利率的价值0.989113 减去 1美元,再乘以真实的本金5000000即可得到最后的−54,437

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