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航 · 2020年08月01日

问一道题：NO.PZ2020021204000034 [ FRM I ]

  1. FRM I
  2. Financial Markets And Products

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.


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.

你好 这道题的时间点不太明白 有一个解答是这样说的 “因为AI的计算应该从上一个付息点开始，这道题目上一个付息点不是2018年12月，是2018年10月15日，所以到2019年4月15的AI就是2。2018年12月的AI是约等于1.” 付息点为什么是2018年10月15日呢？能给个具体的AI计算吗。而且题目里的解析还有把4.5年约算成三个月又是为什么？题目里解析算七年三个月的dirty price 用的是i从0到14,这里的14我认为是7年每半年给一次coupon，7年一共是14次coupon折现。那剩下的三个月题目解析里给的是the dirty price of the bond three months earlier是89.3732. 但是算90.7039的时候就没考虑多出来的三个月，那为什么要折现呢？问题有点多 这道题实在是想不明白 多谢啦
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航 · 2020年08月01日

再补充一下 之前提问了“而且题目里的解析还有把4.5年约算成三个月又是为什么？”这里有个笔误 应该是“而且题目里的解析还有把4.5月约算成三个月又是为什么？”。还有一点我觉得我可能想明白了 因为是2026年4月15号到期 比如算AI的时候 coupon就是按照这个日期往前推半年就是10月15号。

1 个答案

品职答疑小助手雍 · 2020年08月02日

嗨，努力学习的PZer你好：


因为要交割债券的付息时点是4月15号，半年付息的话那每年就是4月15和10月15两个日子付息。这题简化了计算（把10月15号到12月的时间约等成了3个月）。一年4的coupon，3个月就是1。这题这么计算是因为原版书的出题人懒，考试不会出这么麻烦的时间节点的，放心。

最后一个问题没明白你的意思，这题说白了就是求18年底的clean price，计算过程就是把2026年4月15号到期的债券折7年零3个月到2018年底（求出dirty price），然后减掉AI（约等于1），就算出clean price了，最后一步它是先折了7整年，算出一个value，然后把这个value再折3个月，总共折了7年零3个月。


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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！


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