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幸运是努力带来的 · 2022年04月03日

为什么要折现

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

为什么A不对?为什么要折现? 折现之后是零起点的现值,为什么不是付息日和到期日的现金流?

1 个答案

品职答疑小助手雍 · 2022年04月03日

同学你好,本题相当于把债券看成两个零息债了,mapping是为了求var,是要通过价格对利率的敏感性来算var的,当然要折现求价格。

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