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Danlei · 2021年10月24日

对于期间有现金流产生的情况,为何适用这个方法呀?

NO.PZ2020021204000050

问题如下:

Suppose that the six-month Libor rate is 5%, the forward Libor rate for the period between 0.5 and 1.0 year is 5.6% and the forward Libor rate for the period between 1.0 and 1.5 years is 6.0. The two-year Libor swap rate is 5.7%. All risk-free rates are 4.5%., what is the 1.5-year Libor zero rate expressed with semi-annual compounding?

选项:

解释:

Using six-month forwards, 100 would grow to:

100 X (1 + 0.05/2) X (1 + 0.056/2) X (1 + 0.06/2) = 108.5311

If R is the 1.5 year zero rate with semi-annual compounding:

100 X (1 + R/2)^3 = 108.5311

This can be solved to give R = 0.055329. The zero rate is

5.5329%.

在与本题相关联的上一题中,有一个老师给出的解答中,有提及到,本题的解题思路适用的情况是期间没有现金流产生,然后利息最后一次结清。但是对于swap来讲,期间是有现金流产生的,需要适用FRA的思路。

这个说法不是与本题的思路矛盾么?

我的理解有问题吗?请老师解答下疑惑。感谢。

1 个答案
已采纳答案

李坏_品职助教 · 2021年10月25日

嗨,从没放弃的小努力你好:


你问的这一道题和FRA的现金流没什么关系,这道题是求zero rate,不需要考虑现金流。可以看一下讲义P593.


上一道题求的是libor rate,所以需要按照不同的FRA合约的value加起来等于0,反推出libor rate。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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NO.PZ2020021204000050问题如下Suppose ththe six-month Libor rate is 5%, the forwarLibor rate for the periobetween 0.5 an.0 yeis 5.6% anthe forwarLibor rate for the periobetween 1.0 an1.5years is 6.0. The two-yeLibor swrate is 5.7%. All risk-free rates are4.5%., whis the 1.5-yeLibor zero rate expressewith semi-annucompounng?p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #464247}span.s1 {color: #4b6f}span.s2 {color: #67564span.s3 {color: #2f456b}Using six-month forwar, 100 woulgrow to:100 X (1 + 0.05/2) X (1 + 0.056/2) X (1 + 0.06/2) = 108.5311If R is the 1.5 yezero rate with semi-annucompounng:100 X (1 + R/2)^3 = 108.5311This csolveto give R = 0.055329. The zero rate isp.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #493e41}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4134}span.s1 {font: 6.0px Helvetica}span.s2 {color: #43525f}span.s3 {color: #505e72}span.s4 {font: 8.5px Helvetica}5.5329%.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464047}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #453f4b}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443f46}span.s1 {color: #3a4567}span.s2 {color: #6b554c}span.s3 {color: #545867}span.s4 {color: #7b7979}span.s5 {color: #63524span.s6 {color: #736b67}span.s7 {color: #4a576a}span.s8 {font: 8.5px Helvetica}span.s9 {color: #67564老师好,libor zero rate居然是零息债券利率吗?

2024-07-03 22:18 1 · 回答

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