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.
No.PZ2020021204000019 (问答题)
来源: 原版书
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.
解析
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.
问题：为什么求二阶导的时候用的是modified convexity（=6.9020）而不是convexity（=7.9021），课上说的公式用的是convexity
