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Cooljas · 2024年04月18日

这个权重为什么是这样算的啊?

NO.PZ2023091701000051

问题如下:

A risk manager at a bank is measuring the sensitivity of a bond portfolio to non-parallel shifts in spot rates. The portfolio currently holds a 4-year zero coupon bond and a 7-year zero coupon bond with the following sensitivities to these respective spot rates:


To model the non-parallel movement of the spot rate curve, the manager treats the 2-year, 5-year, and 10-year spot rates as key rates. Given this information, what is the portfolio’s key rate 01 (KR01) for a 1-bp increase in the 5-year rate?

选项:

A.AUD 184.06 B.AUD 226.99 C.AUD 307.66 D.AUD 491.72

解释:

C is correct. For a key rate (or partial) 01, the magnitude of a shift in a key rate declines linearly to zero at the next key rate above and/or below. Therefore, if the 5-year spot rate increases by 1 bp, the 4-year and 7-year spot rates change as follows:

4-year spot rate:

7-year spot rate:

The change in the value of the portfolio for a 1 bp change in the 5-year spot rate is therefore:

0.6667189.27+0.6302.45=307.6563

A is incorrect. This incorrectly calculates the changes in the 4-year and 7-year rates as 0.3333 and 0.4 respectively.

B is incorrect. This incorrectly calculates the change in the 7-year rate as 0.3333.

D is incorrect. This incorrectly calculates the forward bucket 01 for the portfolio, assuming the 4-year and 7-year rates change by 1.



3 个答案

品职答疑小助手雍 · 2024年04月24日

第四年……,你是想用7年和10年的算4年的么?我第一次回答时候写的,因为4在2和5之间,要用最近期限的利率去估计。

品职答疑小助手雍 · 2024年04月23日

一样的道理啊,7年在5年和10年之间,位置的比例就像相似三角形一样,(10-7)/(10-5)

Cooljas · 2024年04月23日

如果类比第四年的,为啥不是(7-5)/(10-5)啊?

品职答疑小助手雍 · 2024年04月19日

同学你好,它这个不能说是权重,是类似线性插值法的方法进行的计算,4年的spot相当于是:0.6667的5年的利率变化影响 加上 1-0.6667=0.3333的2年的利率变化影响得到的。

因为4年在 2年和5年之间,三分之二的位置,即解析里用的(4-2)/(5-2)=0.6667

Cooljas · 2024年04月22日

为啥7-year spot rate的分母是10-7啊?

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