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Amy · 2021年04月07日

题目中怎么可以看出用连续复利的方法折现呢?

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

题目中怎么可以看出用连续复利的方法折现呢?

2 个答案
已采纳答案

品职答疑小助手雍 · 2021年04月08日

嗨,从没放弃的小努力你好:


frm里的折现没有硬性规定,可以复利折现也可以连续复利折现,结果差不太多。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

王楚溪 · 2021年09月08日

可是这道题用单利的话,答案差的还挺多的呀,0.04/(1+3.5%)+1.04/(1+4.5%)^2这样算出来最终结果是-44969,答案就不知道选什么了。另外为什么基础班讲义上的例题就用的是单利?难道是用libor折现就用单利,没有提到libor就用连续复利吗?

品职答疑小助手雍 · 2021年09月08日

这个不同方法差异方面不用太担心,考试时候选项肯定可以轻松辨认出来的。

你用的这个折现方法是复利的,题目解析用的是连续复利。

(1+X%*2)这种形式的才是单利。libor只是计息用的是单利,折现不会用单利的。除非有省事的简便计算之类的(不算太严谨的情况下)。

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