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Brian邵彬 · 2024年11月06日

一点疑问

  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.

这道题，按照时间的平方乘以权重去算凸性，凸性我算怎么等于7.9014，然后除以1.07的呀等于7.3845，不等于6.902啊



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1 个答案

李坏_品职助教 · 2024年11月06日

嗨，爱思考的PZer你好：


上面那个convexity计算的等式写错了，应该是时间的平方 * 权重，然后除以(1+7%)^2 。


先求出债券的价格 = 10/1.07 + 10/1.07^2 + 110 / 1.07^3 = 107.8730

权重计算如下：

比如time 1的权重 = 第一年的现金流PV / 债券价格107.8730 = 8.67%.

然后convexity = (1^2 * weight1 + 2^2 * weight2 + 3^2 * weight3) / 1.07^2 =6.90.



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