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薛真 · 2020年03月16日

问一道题: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.

-2.5661,6.9020这两个数字怎么算的?

1 个答案

品职答疑小助手雍 · 2020年03月16日

同学你好,这个计算需要掌握原理,但是实际考试计算量很难有这么大所以不会考,过程如下:

通常是用modified duration:也就是2.7458/1.07=2.5661

convexity是用7.9021/(1.07的平方)=6.902

薛真 · 2020年04月04日

1.07指的是107.8729吗

品职答疑小助手雍 · 2020年04月07日

1.07指的是1+r

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