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hyi725 · 2022年08月06日

年化360/180是因为coupon半年付一次吗？

  1. CFA II
  2. Derivative

NO.PZ2019010402000061

问题如下：

Suppose one year ago we entered a €200,000,000 three-year receive-fixed Libor-based interest rate swap with semi-annual resets (30/360 day count). The fixed rate in the swap contract entered one year ago was 4.5%. The value for the party receiving the fixed rate is:

选项：

A.- €648,079.61 B.

€648,079.61

C.

- €548,068.57

解释：

B is correct

本题考察的是利率互换求value。

先求出在t=1时刻的互换的固定利率：

∑i=1nPVi(1)=0.985222+0.966184+0.943396+0.917431=3.812233\sum_{i=1}^nPV_i\left(1\right)=0.985222+0.966184+0.943396+0.917431=3.812233

fixed swap rate = (1- 0.917431) / 3.812233=2.1659%

annulized: 2.1659% * 360/180 = 4.3318%

然后计算value，对于fixed receiver：

V= (0.045 - 0.0433) ×(180/360)×3.812233×200,000,000 = €648,079.61

年化的时候不小心写成了 x 180/360 如何区分呢？

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1 个答案

Lucky_品职助教 · 2022年08月07日

嗨，爱思考的PZer你好：


1、年化360/180是因为coupon半年付一次吗？--是的

2、年化的时候不小心写成了 x 180/360 如何区分呢？

360/180叫年化，我们有时候算出来的是一段区间的利率，但题目问的是年化利率，这时候我们除以这段区间，乘以360，就变成按年来看的利率

180/360是我们有时候用的是年化利率，但要算某一段区间的value，因为我们可能没有持有一整年，就需要除以360，再乘以区间天数

本题就是先把利率年化了，算value的时候又去年化了~


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