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水瓶公主 · 2023年03月07日

折现之后减去现值是互换的价值吗？

  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

互换价值


为什么有的题目折现完就是互换价值呢

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1 个答案

李坏_品职助教 · 2023年03月07日

嗨，努力学习的PZer你好：


利率互换是一方收取浮动利息，同时支付固定利息。另一方反过来。所以对于收取固定利息的一方来说，他的净现金流的现值=NPV固定利息 - NPV浮动利息，这个就是利率互换的价值。


只要是利率互换，求价值必然都是现值相减。你说的折现之后就是价值的可能是FRA合约，那是另一种产品了。

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