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水瓶公主 · 2023年03月07日

用4.5%折现到0时刻也可以吗

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?

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%.

往前折现法也可以吧?

1 个答案

李坏_品职助教 · 2023年03月07日

嗨,爱思考的PZer你好:


这道题求的是zero rate,zero rate就是spot rates, 指的是零息债券的到期收益率:

题目问的是1.5年的zero rate,现值是100,我们需要利用远期利率求出终值108.53,在计算100到108.53之间的半年复利利率。

题目给的4.5%是无风险利率,题目求的是libor的zero rate,4.5%没啥用。

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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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