NO.PZ2020011303000242
问题如下：
Calculate the forward bucket 01s for a two-year bond with a coupon of 8% and a face value of USD 10,000 when the there are two buckets: 0–1 year and 1–2 year. Assume that the term structure is flat at 4% (semi-annually compounded).
解释：
The value of the bond is
400/1.02+400/1.022 +400/1.023 +10,400/1.024 = 10,761.5457
When the forward rates in the first bucket increase by one basis point, the value of the bond becomes
400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)= 10,760.5100
This is a decrease of 1.0358. When the forward rates in the second bucket increase by one basis point, the value of the bond becomes
400/1.02+400/1.022+400/(1.022×1.02005)
+10,400/(1.022×1.020052) = 10,760.5854
This is a decrease of 0.9604. The forward bucket 01s are therefore 1.0358 and 0.9604.
题目问：2年期的债券coupon rate是8%，面值是10k，当有2个buckets：0-1年和1-2年时，计算forward bucket 01s。假设利率的期限结构是flat，4%的利率，半年付息一次。
债券价格：
= 400/1.02+400/1.022 +400/1.023 +10,400/1.024
= 10,761.5457
当0-1年的bucket的forward rate上升1bp时，债券价格变成：
= 400/1.02005+400/1.020052 +400/(1.020052×1.02)+10,400/(1.020052×1.022)
= 10,760.5100
价格下降了1.0358.
当1-2年的bucket的forward rate上升1bp时，债券价格变成：
=400/1.02+400/1.022+400/(1.022×1.02005)+10,400/(1.022×1.020052)
= 10,760.5854
价格下降了0.9604.
The forward bucket 01s 为 1.0358 和 0.9604.
我记得老师上课给我们讲过题的思路 然后说基本计算考的概率很低 所以不太需要掌握？
