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Roseline · 2020年12月24日

问一道题：NO.PZ2018122701000042

  1. FRM II
  2. Market Risk Measurement And Management

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

老师好，题目说了是半年付息，在求12个月的mapping position的时候，折现率为什么不是用2.5%/2?


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小刘_品职助教 · 2020年12月25日

同学你好，

因为题目是把半年付息的债券mapping成零息债券，而这2.5%就是1年对应的利率，所以不能用你这方法算。

朵朵0927 · 2022年06月05日

老师，请教下，因为一级都不太记得了，什么情况下是（1+2.5%/2)的平方？

品职答疑小助手雍 · 2022年06月06日

单个债券半年付息的话，求它的pv可以（1+2.5%/2)的平方

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