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lion · 2023年04月03日

求解释

  1. FRM I
  2. Financial Markets And Products

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  =0.04e−0.035+1.04e−0.045×2=0.989113B_{fix}\;=0.04e^{-0.035}+1.04e^{-0.045\times2}\\=0.989113

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

请问这个公式是什么意思，是哪里的知识点

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1 个答案

李坏_品职助教 · 2023年04月03日

嗨，爱思考的PZer你好：


这个考点是利率互换的valuation。


公式里面Bfix表示收取固定利息这个部分的价值（类似于一个普通债券的定价），这里是假设Swap的面值是1美元。所以收取固定利息部分的Bfix = 每期利息0.04*exp(-3.5%) + 期末本息之和1.04*exp(-4.5%*2) = 0.989113. 这个结果表示1美元的本金对应的收取固定利息部分的现值是0.989113美元。


利率互换的浮动利息部分的价值在reset date（题干末尾告诉我们的）一定是1，所以最后直接用0.989113-1，再乘以面值5million即可。


讲义里的例题（Valuing a Plain Vanilla Swap）思路和这个类似，只是收取固定利息部分的计算方法不一样：

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