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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。

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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已采纳答案

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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