James · 2024年02月15日
NO.PZ2023052301000046
问题如下：
Consider a bond that has three years remaining to maturity, a coupon of 4% paid semiannually, and a yield-to-maturity of 4.60%. Assuming it is 12 days into the first coupon period and a 30/360 basis, the bond’s annualized Macaulay duration is closest to:
选项：
A.
1.8764 years.
B.
2.8386 years.
C.
2.8553 years.
解释：
B is correct.
我是按折现到0时刻的pv来算的，算出来是2.8553，然后因为有t的因素，所以推断久期还要再短一点点，所以选B。但是让我计算带小t的久期就不会了…
李坏_品职助教 · 2024年02月16日
嗨，努力学习的PZer你好：
其实带不带t差距不大。
你看答案解析里面第二列，距离第一次支付利息还剩180-12 = 168天，也就是Time to Receipt = 168/180=0.9333。
距离第二次支付利息还剩168 + 180 = 348天，也就是Time to Receipt = 168/180 + 1 =1.9333。
这里的1代表1个半年，0.9333表示0.9333个半年。
找到每一个Time to Receipt之后，再计算PV。第一行的PV = 2 / (1+4.6%/ 2)^(0.9333) = 1.958.
第二行的PV = 2/(1+4.6%/2)^(1.9333) = 1.9340.
以此类推计算出每一个PV，求和之后得到98.4856，然后再去计算weight。最后用每一行的weight * Time to Receipt就得到了MacDur，除以2就得到年化的Annualized MacDur.
----------------------------------------------虽然现在很辛苦，但努力过的感觉真的很好，加油！
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