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上小学 · 2023年04月12日

请问这个题具体有什么思路吗?我听讲义也没弄明白怎么解转换系数?

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.


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.

烦请具体写下该类题怎么解答,多谢。


2 个答案

李坏_品职助教 · 2023年04月12日

嗨,从没放弃的小努力你好:


考试应该不会考这么复杂,可以记一下最后那个公式:

债券的全价 = 最近期的债券期货价格 * conversion factor + Accrued Interest,就差不多了。

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努力的时光都是限量版,加油!

李坏_品职助教 · 2023年04月12日

嗨,从没放弃的小努力你好:


转换因子conversion factor的定义:

conversion factor就是对于一个1美元面值的债券,假设所有利率(折现率)都是6%、半年复利的情况下,这个债券的净价。

根据下面的公式,债券的价格(全价,包含了Accrued Interest) = 最近期的债券期货价格 * conversion factor + Accrued Interest(应计利息),

所以这种题目需要先求出债券的全价, 本题中,债券的现金流如下:

先算出到2019.4的债券全价是90.7039(4.5个月近似看作3个月,这样方便计算)。然后从2019.4折现到2018.12,也就是90.7039/根号下(1.03) = 89.3732

所以89.3732 = 期货价格(默认为100) * cf + 应计利息1块钱,所以cf = 88.3732 / 100 = 0.8837.

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上小学 · 2023年04月12日

谢谢,这个题太复杂了。如果考试可能性不大还是复习其他科目更有用。

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