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JiangHan · 2023年02月13日

债券价格的折现可以按时间分开折吗

NO.PZ2020021204000034

问题如下:

A bond that can be delivered in the December 2018 ten-year Treasury note futures contract is a bond with maturity on April 15, 2026, that pays a coupon of 4% per annum.When the yield is 6% per annum(with semi-annual compounding) , calculate the conversion factor for the bond.


选项:

解释:

The bond's time to maturity on the first day of the delivery months is seven years (December 2018 to December 2025) and 4.5 months (January 2026 to mid-April 2026).This is rounded to seven years and three months. The dirty price of a seven year and three-month bond immediately before the coupon payable in three months is

i=01421.03i+1001.0314=90.7039\sum_{i=0}^{14}\frac2{1.03^i}+\frac{100}{1.03^{14}}=90.7039

when the yield is 6%. The dirty price of the bond three months earlier is

90.70391.03=89.3732\frac{90.7039}{\sqrt{1.03}}=89.3732

Subtracting the accrued interest of 1, we get a clean price of 88.3732 and the conversion factor is 0.8837.

这个题的解析里面,先折了7年的,又折了三个月的,可以这样做吗,还有类似的这样的题吗

3 个答案
已采纳答案

DD仔_品职助教 · 2023年02月14日

嗨,从没放弃的小努力你好:


确实是先往前折7年,然后又折3个月,不好意思同学。。。

这样算的主要原因就是我们求债券价格的时间点不是付息日,也不是刚发行的那一天,所以用这种方法。

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加油吧,让我们一起遇见更好的自己!

DD仔_品职助教 · 2023年02月14日

嗨,努力学习的PZer你好:


这个债券从2018年12月到2026年4月还有大概7年零3个月到期,付息日是每年的4月和10月,所以我们讲付息日的现金流先用半年利率挨个折现,我们只能折到7年,还需要再往前折3个月,所以第二步将所有现金流又往前折了3个月。

你不需要记住,但是需要读题,题目说了是2026年4月到期,并且是半年付息一次,那么就可以推断出来是每年4月和10月付息。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

JiangHan · 2023年02月14日

好的老师,可这不就是先折七年再往前折三个月吗

DD仔_品职助教 · 2023年02月13日

嗨,爱思考的PZer你好:


同学你好,

这里不是先折7年又折三个月,而是不同时间点发生的现金流依次进行折现。

这个债券从2018年12月到2026年4月还有大概7年零3个月到期,付息日是每年的4月和10月,我们这个式子求的是2019年4月刚好在付息日前这一时刻的价格,这个答案的式子写的不够清楚,我们把式子拆开可以写成:

=2+2/(1+3%)^2+2/(1+3%)^3+....+2/(1+3%)^14+100/(1+3%)^14=90.7039

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努力的时光都是限量版,加油!

JiangHan · 2023年02月13日

那它解析的第二步,为什么要再用三个月折一次呢 还有我该怎么知道这个债券的付息日是4月和10月呢,是要记住吗(针对什么类型的债券呢)

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