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菜农 · 2023年02月21日

关于几天前老师回答 同学的问题中凸性计算的公式的疑问

  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.



老师您好，想请问下convexity的计算公式，为什么是 time*weight^2/(1+YTM)?


convexity那一节中，李老师给的convexity的计算公式是：

time^2*weight

如下图所示




请问这两种计算convexity的方式哪个是正确的呢？感谢！


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1 个答案

李坏_品职助教 · 2023年02月21日

嗨，从没放弃的小努力你好：


这个算法是有问题的，以李老师的算法为准。


李老师的算法是对的，而且也是和原版书教材里的保持一致：

注意这里求出来的8.13904是原始版convexity，还要除以（1+YTM）^2才是modified convexity。

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