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比如世界 · 2020年02月24日

问一道题:NO.PZ2020021204000034 [ FRM I ]

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. 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.

老师你好,这道题没有什么思路,可以再讲一下考点吗,谢谢

1 个答案

品职答疑小助手雍 · 2020年02月24日

同学你好,这题归根结底求得是clean price。因为期货交割是以quoted(clean) price作为报价的。因为这里Treasury note期货到期交割面值100,所以conversion factor*100=clean price,就能得出这题求的conversion factor=clean price/100。

求clean price的方法,这题少了个条件就是YTM是6%(回头反馈下补上),就是已知YTM=6%,coupon rate是4%,题目近似求了T=7.25年,条件已知,方法见讲义part2的66-69页。

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