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Brian邵彬 · 2025年01月03日

一点疑问

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000243

问题如下：

A two-year bond with a coupon of 8% and a face value of USD 10,000. There are two buckets: 0-1 year and 1-2 year, and the forward bucket 01s are 1.0358 and 0.9604 correspondingly.

Assume that the term structure is flat at 4% (semi-annually compounded).

Convert the forward bucket 01s to durations.

选项：

解释：

The value of the bond is

4001.02+4001.022+4001.023+10,4001.024=10,761.5457\frac{400}{1.02}+\frac{400}{1.02^2}+\frac{400}{1.02^3}+\frac{10,400}{1.02^4}=10,761.5457

The duration measure for the first forward bucket is

10,000×1.035810,761.5457=0.9625\frac{10,000\times1.0358}{10,761.5457}=0.9625

The duration measure for the second forward bucket is

10,000×0.960410,761.5457=0.8924\frac{10,000\times0.9604}{10,761.5457}=0.8924


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，forward bucket 01s 为 1.0358 和 0.9604.

假设利率的期限结构是flat，4%的利率，半年付息一次。请将forward bucket 01s转化成为durations。

duration=面值*forward bucket 01/债券价格

可以0.9604+1.8549去算一个总的duration么，这么做有经济意义么

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1 个答案

李坏_品职助教 · 2025年01月03日

嗨，爱思考的PZer你好：


0.9604这个不是duration，这个是forward bucket 01。这道题就是想让你把forward bucket 01转化为duration。


duration = forward bucket 01 * 10000 / value。


你把这俩相加没有什么意义。

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NO.PZ2020011303000243 问题如下 A two-yebonwith a coupon of 8% ana favalue of US10,000. There are two buckets: 0-1 yean1-2 year, anthe forwarbucket 01s are 1.0358 an0.9604 corresponngly.Assume ththe term structure is fl4% (semi-annually compoun. Convert the forwarbucket 01s to rations. The value of the bonis 4001.02+4001.022+4001.023+10,4001.024=10,761.5457\frac{400}{1.02}+\frac{400}{1.02^2}+\frac{400}{1.02^3}+\frac{10,400}{1.02^4}=10,761.54571.02400​+1.022400​+1.023400​+1.02410,400​=10,761.5457The ration measure for the first forwarbucket is10,000×1.035810,761.5457=0.9625\frac{10,000\times1.0358}{10,761.5457}=0.962510,761.545710,000×1.0358​=0.9625The ration measure for the seconforwarbucket is10,000×0.960410,761.5457=0.8924\frac{10,000\times0.9604}{10,761.5457}=0.892410,761.545710,000×0.9604​=0.8924题目问2年期的债券couponrate是8%，面值是10k，当有2个buckets0-1年和1-2年时，forwarbucket 01s 为 1.0358 和 0.9604.假设利率的期限结构是flat，4%的利率，半年付息一次。请将forwarbucket 01s转化成为rations。ration=面值*forwarucket 01/债券价格 ration=面值*forwarbucket 01/债券价格这里为什么不是value而是面值？

2024-04-22 23:05 1 · 回答

NO.PZ2020011303000243问题如下 A two-yebonwith a coupon of 8% ana favalue of US10,000. There are two buckets: 0-1 yean1-2 year, anthe forwarbucket 01s are 1.0358 an0.9604 corresponngly.Assume ththe term structure is fl4% (semi-annually compoun. Convert the forwarbucket 01s to rations. The value of the bonis 4001.02+4001.022+4001.023+10,4001.024=10,761.5457\frac{400}{1.02}+\frac{400}{1.02^2}+\frac{400}{1.02^3}+\frac{10,400}{1.02^4}=10,761.54571.02400​+1.022400​+1.023400​+1.02410,400​=10,761.5457The ration measure for the first forwarbucket is10,000×1.035810,761.5457=0.9625\frac{10,000\times1.0358}{10,761.5457}=0.962510,761.545710,000×1.0358​=0.9625The ration measure for the seconforwarbucket is10,000×0.960410,761.5457=0.8924\frac{10,000\times0.9604}{10,761.5457}=0.892410,761.545710,000×0.9604​=0.8924题目问2年期的债券couponrate是8%，面值是10k，当有2个buckets0-1年和1-2年时，forwarbucket 01s 为 1.0358 和 0.9604.假设利率的期限结构是flat，4%的利率，半年付息一次。请将forwarbucket 01s转化成为rations。ration=面值*forwarucket 01/债券价格 请问一下为什么这里的ration不带负号呢？

2024-03-31 20:57 1 · 回答

NO.PZ2020011303000243 这一题，以及前面一个题，都没太看懂。 请问这个考点的计算，重要么？

2021-10-30 17:11 1 · 回答

Assume ththe term structure is flat 4% (semi-annually compoun ——这是什么意思？没有读懂题目，也不懂这里考的啥

2020-04-12 22:08 1 · 回答