如何判断方向？

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

- €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：

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

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

为什么是0.045-0.043348？为什么不是反过来？我方向算反了

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1 个答案

pzqa35 · 2023年10月24日

嗨，爱思考的PZer你好：

这道题考察的时swap的估值。题目中表述为receive-fixed Libor-based interest rate swap，所以是一个pay floating，receive fixed的互换合约。投资者在0时刻签订的是收年华4.5%的固定利息，到了1年这个时间点，我们想来看一下这个合约的value就是要签订一个反向头寸，也就值支付固定，收到浮动的2年期的swap。那么浮动端会抵消掉，固定端就是收到年化4.5%，支付年化4.3318%，所以利差就是0.045 - 0.0433。

对于互换合约，我们最先需要判定的就是头寸，本题的头寸和我们平时的支付固定、收到浮动的swap刚好是相反的，所以要反向来操作，或者按照支付固定、收到浮动的swap进行估值后加上负号也可以。

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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！

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NO.PZ2019010402000061 问题如下 Suppose one yeago we enterea€200,000,000 three-yereceive-fixeLibor-baseinterest rate swwithsemi-annuresets (30/360 y count). The fixerate in the swcontractentereone yeago w4.5%. The value for the party receiving the fixerateis: A.- €648,079.61 B.€648,079.61 C.- €548,068.57 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∑i=1nPVi(1)=0.985222+0.966184+0.943396+0.917431=3.812233fixeswrate = (1- 0.917431) / 3.812233=2.1659%annulize 2.1659% * 360/180 = 4.3318%然后计算value，对于fixereceiverV= (0.045 - 0.0433)×(180/360)×3.812233×200,000,000 = €648,079.61

2024-07-16 17:10 1 · 回答

NO.PZ2019010402000061问题如下 Suppose one yeago we enterea€200,000,000 three-yereceive-fixeLibor-baseinterest rate swwithsemi-annuresets (30/360 y count). The fixerate in the swcontractentereone yeago w4.5%. The value for the party receiving the fixerateis: A.- €648,079.61B.€648,079.61C.- €548,068.57 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∑i=1nPVi(1)=0.985222+0.966184+0.943396+0.917431=3.812233fixeswrate = (1- 0.917431) / 3.812233=2.1659%annulize 2.1659% * 360/180 = 4.3318%然后计算value，对于fixereceiverV= (0.045 - 0.0433)×(180/360)×3.812233×200,000,000 = €648,079.61 请问如何判断正负? 我理解是作为fixereceiver 一年前定价4.5相当于收到4.5,现在重新定价4.33 ，收到少了，所以是亏了，请问哪里不对呢？

2024-04-11 22:47 1 · 回答

NO.PZ2019010402000061问题如下 Suppose one yeago we enterea€200,000,000 three-yereceive-fixeLibor-baseinterest rate swwithsemi-annuresets (30/360 y count). The fixerate in the swcontractentereone yeago w4.5%. The value for the party receiving the fixerateis: A.- €648,079.61B.€648,079.61C.- €548,068.57 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∑i=1nPVi(1)=0.985222+0.966184+0.943396+0.917431=3.812233fixeswrate = (1- 0.917431) / 3.812233=2.1659%annulize 2.1659% * 360/180 = 4.3318%然后计算value，对于fixereceiverV= (0.045 - 0.0433)×(180/360)×3.812233×200,000,000 = €648,079.61 画图法能做吗，能不能画一下，我算的和答案有出入

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如何判断方向？

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