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Brian邵彬 · 2024年11月07日

有点疑问

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.

10年债券,到期日是2026年4月15,起始日是2016年4月25?每半年付息一次,那在delivery date,也就是2018年12月的时候,上一次付息是在2018年10月15日?那应计利息应该是2018年10月15日到2018年12月?为什么答案说是18年12月到19年4月之间的利息?

3 个答案

李坏_品职助教 · 2024年11月07日

嗨,努力学习的PZer你好:


是的

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努力的时光都是限量版,加油!

李坏_品职助教 · 2024年11月07日

嗨,努力学习的PZer你好:


应该是这样的:

求出在2019.04的价格之后,再往前折现到2018.12得到P0 = P1 / 根号1.03 = 89.3732,这个P0是dirty price。


最后减去AI=1,这个AI指的是从上一次支付coupon(2018.10)到现在交割日积累的应计利息。由于题目中从交割日到下一次支付coupon看做3个月,那么交割日到上一次支付coupon的时间也是3个月,所以最后减去的AI = 1。

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努力的时光都是限量版,加油!

Brian邵彬 · 2024年11月07日

所以不是2018.12到2019.04之间的AI,而是2018.10到2018.12之间的AI对吧

李坏_品职助教 · 2024年11月07日

嗨,从没放弃的小努力你好:


我们求的价格是在2018年12月,这个时间点不是付息日,所以我们要先求出在付息日2019年4月这个时间点的价格,在这个点刚好有一笔coupon,所以在求价格的时候是一共有15笔coupon,并且第一笔刚好在2019年4月,具体可以参考下图:

求出在2019.04的价格之后,再往前折现到2018.12得到P0 = P1 / 根号1.03 = 89.3732

而这个P0是dirty price,那就减去2018.12到2019.04之间的AI,也就是89.3732 - 1=88.3732,这才是最后的clean price。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Brian邵彬 · 2024年11月07日

您再看看我的问题,我的意思是如果2018.12是交割的日子,那是不是应该算交割前的应计利息?也就是2018.10到2018.12的这段时间的利息?

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