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12345678wdv · 2024年02月28日

The actual bond price decline is 4.0419

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000019

问题如下：

A three-year bond with a face value of USD 100 pays coupons annually at the rate of 10% per year. Its yield is 7% with annual compounding., estimate the price change if the annually compounded yield changes from 7% to 8.5%, using both the duration and the duration plus convexity approximations.

选项：

解释：

Using duration, the price change is

-2.5661 X 107.8729 X 0.015= -4.1522

Using duration and convexity, it is

-2.5661 X 107.8729 X 0.015 + (1/2) X 6.9020 X 107.8729 X 0.0152 = -4.0685

The actual bond price decline is 4.0419, showing that duration plus convexity gives a better estimate than convexity alone.

这个是在哪里体现的

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1 个答案

李坏_品职助教 · 2024年02月28日

嗨，爱思考的PZer你好：


这个是具体计算出来的。

当收益率为7%时，债券价格=10 / 1.07 + 10/1.07^2 + 110/1.07^3 = 107.87295.

当收益率变为8.5%时，债券价格 = 10/1.085 + 10/1.085^2 + 110/1.085^3 = 103.83103.


所以当利率从7%变为8.5%时，债券价格变动比率=103.83103 - 107.87295 = -4.0419.

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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