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· 2022年02月08日

还是有些问题不懂

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.

看了老师对于其他问题的解答,仍然有三个方面不明白:

  1. 请问为什么要将4.5个月就近折成3个月呢?直接4.5/6 按照比例进行复利不就可以了吗
  2. 请问首项为什么是2除以(1.03)^2呢,如果是三个月,不应该是1/2而不是2吗?
  3. 请问为什么第二项的分子时100而不是102呢?这个后面就不需要计算coupon了吗?

问题有点多,主要是仍然不明白这个解题思路,烦请老师进行解惑,多谢耐心~~

1 个答案

品职答疑小助手雍 · 2022年02月08日

同学你好,1.这个点解析里近似了,想起来会方便一丢丢,不过毕竟考试不会出问答题,选择题的答案估计是会按不近似的数计算,不过近似可以帮助选出正确答案,不会因为近不近似导致选项不同。

2和3、解析分了两步,先折7年,再折3个月,所以先折了14个coupon和100的本金; 然后第二步把得到的结果折了3个月得到dirty price。

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