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上小学 · 2023年04月11日

麦考林久期计算多次等于2，28。债券价格等于129，74，三期现金流按照0，07折现，权重乘以时间。

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000018

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. What are (a) the Macaulay duration, (b) the convexity, (c) the modified duration, and (d) the modified convexity?

解释：

The Macaulay duration is 2.7458, the convexity is 7.9021,

and the modified duration is

2.7458 / 1.07 = 2.5661

The modified convexity is

7.9021/1.072 = 6.9020

认为自己计算完全没有错误了，但是答案不对。烦请列一下步骤。谢谢

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品职答疑小助手雍 · 2023年04月11日

同学你好，债券价格：iy=7，PMT=10，n=3 求得PV=107.87.

总共3笔现金流：

第一年末现金流的PV=10/1.07=9.3458

第二年末现金流的PV=10/1.07的平方=8.7344

第三年末现金流的PV=110/1.07的三次方=89.7928。

Mac duration=（9.3458*1+8.7344*2+89.7928*3）/107.87 = 2.7458

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