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葛文君 · 2020年09月14日

问一道题：NO.PZ2020011303000217 [ FRM I ]

  1. FRM I
  2. Valuation And Risk Models

问题如下：

Why is yield-based convexity likely to be greater than yield-based duration for a ten-year bond (assume that rates are expressed with continuous compounding)?

解释：

Yield-based convexity is calculated by squaring each cash flow’s time to maturity and then taking a weighted average with weights proportional to the present values of the cash flows. Yield-based duration is a weighted average of the time to maturity of cash flows with the same weights. For a ten-year bond, the former is clearly greater than the later because, for nearly all the cash flows, the square of the time to payment is greater than the time to payment.

不好意思，没看懂答案，涉及的什么考点？
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品职答疑小助手雍 · 2020年09月14日

嗨，从没放弃的小努力你好：


就是covexity和duration的计算方法问题：

convexity是通过每个现金流占PV的比例，乘以它本身离当前时间的平方得到的。

duration是通过每个现金流占PV的比例，乘以它本身离当前时间得到的。

离到期时间的平方一定比离到期的时间数值大，所以convexity的数值大于duration。


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努力的时光都是限量版，加油！


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