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朵朵0927 · 2022年09月16日

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  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000042

问题如下：

An analyst is using the delta-normal method to determine the VaR of a fixed income portfolio. The portfolio contains a long position in 1-year bonds with a $1 million face value and a 6% coupon that is paid semi-annually. The interest rates on six-month and twelve-month maturity zero-coupon bonds are, respectively, 2% and 2.5%. Mapping the long position to standard positions in the six-month and twelve-month zeros, respectively, provides which of the following mapped positions?

选项：

A.

$30,000 and 1,030,000

B.

$29,500 and 975,610

C.

$29,703 and 1,004,878

D.

$30,300 and 1,035,000

解释：

C is correct.

考点 ： Mapping to Fixed Income Portfolios

解析 ： The long position is mapped into a combination of market values of the zero-coupon bonds that provide the same cash flows:

Xsix=300001+0.02/2=29703X_{six}=\frac{30000}{1+0.02/2}=29703

Xtwelve=10300001+0.025=1004878X_{twelve}=\frac{1030000}{1+0.025}=1004878

老师没有太理解为什么不是 除（ 1+2·5% ）的平方?

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2 个答案

李坏_品职助教 · 2023年03月02日

嗨，爱思考的PZer你好：


因为这里是Mapping到两个零息债，不付利息的，所以直接用X_twelve的本金1030000/ 1.025就好了，没有利息不需要去除以2再平方。

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李坏_品职助教 · 2022年09月16日

嗨，从没放弃的小努力你好：


2.5%是年利率，不是半年的利率。第二个mapping就是要把12个月后的现金流（本金+利息）折现到0时刻，所以直接除以(1+2.5%)就可以了。

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加油吧，让我们一起遇见更好的自己！

kanjani · 2023年03月02日

但它是每半年付息一次 每一笔现金流都应该是年利率/2，再乘n次方啊

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