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Elsa陆艳 · 2022年03月12日

老师您好,中间步骤不太明白

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: 01 year and 12 year. Assume that the term structure is flat at 4% (semi-annually compounded).

选项:

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.

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

第三期和第四期的分母为什么是这样的?还有后面这一步也不太明白。

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) = 10,760.585

1 个答案
已采纳答案

DD仔_品职助教 · 2022年03月13日

嗨,爱思考的PZer你好:


同学你好,

first bucket是0-1年的利率发生变化,1-2年没有,1-2年的第三笔和第四笔现金流进行折现的时候,会经过0-1这个区间,所以用0-1区间的利率折现,具体如下图:

second bucket就是1-2年的利率变化了,0-1年没有,和上面在折现时同理,一笔一笔往前折现要用当期时间段的利率,如下图:

最后一步就是在求价差,利率变化前后,价格的差值就是forward bucket01.

1.0357=10,761.5457-10,760.5100

0.9603=10,761.5457-10,760.5854

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