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梦梦 · 2024年10月07日

swap t时刻求value

NO.PZ2023091802000160

问题如下:

Consider a $1 million notional swap that pays a floating rate based on 6-month LIBOR and receives a 6% fixed rate semiannually. The swap has a remaining life of 15 months with pay dates at 3, 9 and 15 months. Spot LIBOR rates are as following: 3 months at 5.4%; 9 months at 5.6%; and 15 months at 5.8%. The LIBOR at the last payment date was 5.0%. Calculate the value of the swap to the fixed-rate receiver using the bond methodology.

选项:

A.

$6,077

B.

-$6,077

C.

-$5,077

D.

$5,077

解释:


老师,1、题目给的spot libor 不是即期利率吗?我理解spot libor 3个月是站在现在,3个月的利率是5.4%,9个月是站在现在5.6%,也就是0到9月,15个月就是0到15月,但是,对于float来讲,9个月的节点利率应该是第3个月决定的,也就是应该是站在现在,3到9的远期利率啊,15个月的利率应该是在第9个月决定的,也就是站在现在,9到15的远期利率。我想的哪儿错了吗?

2、考试时,给的是libor也会明确说明折现方式吗?还是给的是libor就是用单利折现?


1 个答案
已采纳答案

pzqa39 · 2024年10月08日

嗨,爱思考的PZer你好:


“spot libor 3个月是站在现在,3个月的利率是5.4%,9个月是站在现在5.6%,也就是0到9月,15个月就是0到15月”这句话正确


浮动利率是每个reset period payment决定下一个reset period payment是多少,题目给了t=-3时刻的LIBOR是5%,浮动利率每到一个重置期就重新定一个浮动的利率,这个利率持续到下一个重置期,所以-3时刻的LIBOR是帮助我们确定3时刻的现金流的。浮动利率的现金流在t=3时刻是1m*5%*0.5,之后再按照题目给的3时刻的Spot LIBOR rates(也就是折现率),和1m一起折回0时刻就可以了。

 

LIBOR正常情况下是单利,李老师说了这题用复利不严谨。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

梦梦 · 2024年10月13日

哦哦,明白了,谢谢老师

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