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Maxy · 2024年03月19日

我用计算器按V0算出来的不一样呢？

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000219

问题如下：

Consider a zero-coupon bond with a face value of USD 100 and a maturity of ten years. What is the DV01 and the effective duration when the ten-year rate is 4% with semi-annual compounding? (Consider one-basis-point changes and measure rates as decimals when calculating duration.)

选项：

解释：

The value of the bond is

100/1.0220=67.297133

When the ten-year rate increases to 4.01%, the value decreases by 0.065944 to 67.231190. When the ten-year rate decreases to 3.99%, the value increases by 0.066012 to 67.363145. The DV01 can be estimated as the average of 0.065944 and 0.066012, or 0.065978. The effective duration is 0.065978/(67.297133×0.0001)=9.804

题目问：一个零息债券的面值是100USD，期限是10年，当利率是4%，半年付息一次时，DV01和effective duration是多少？

债券的价格V0=100/(1+4%/2)^(10*2)=67.297133

当利率上升1bp到4.01%时，债券价格V+=100/(1+4.01%/2)^(10*2)=67.23119

价格下降0.065944

当利率下降1bp到3.99%时，债券价格V-=100/(1+3.99%/2)^(10*2)=67.36314

价格上升0.066012

DV01=（0.065944 + 0.066012）/2= 0.065978

effective duration=0.065978/(67.297133×0.0001)=9.804

N=20，I/Y=2, PMT=2, FV=100求PV，是这样吧？

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2 个答案

pzqa27 · 2024年10月12日

嗨，努力学习的PZer你好：


我们需要先计算出V-和V+。其中V-是：当利率下降1bp到3.99%时，债券价格V-=100/(1+3.99%/2)^(10*2)=67.36314。


V+是当利率上升1bp到4.01%时，债券价格V+=100/(1+4.01%/2)^(10*2)=67.23119，


V0就是利率不变的时候的价格100/(1+4%/2)^(10*2)=67.297133。


所以带入公式：effective duration = ((V-) - (V+)) / (2 * V0 * 0.01%)= 9.804

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努力的时光都是限量版，加油！

pzqa27 · 2024年03月20日

嗨，爱思考的PZer你好：


不对啊，题目说的是0息债券，是不会期间有PMT的，正确的算PV方法请按解析的过程计算。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

一只🐶哆啦 · 2024年10月12日

价格上升0.066012 DV01=（0.065944 + 0.066012）/2= 0.065978 effective duration=0.065978/(67.297133×0.0001)=9.804 这里ed应该要➗2吧，我感觉答案错了

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NO.PZ2020011303000219问题如下Consir a zero-coupon bonwith a favalue of US100 ana maturity of ten years. Whis the 01 anthe effective ration when the ten-yerate is 4% with semi-annucompounng? (Consir one-basis-point changes anmeasure rates cimals when calculating ration.) The value of the bonis100/1.0220=67.297133When the ten-yerate increases to 4.01%, the value creases 0.065944 to 67.231190. When the ten-yerate creases to 3.99%, the value increases 0.066012 to 67.363145. The 01 cestimatethe average of 0.065944 an0.066012, or 0.065978. The effective ration is 0.065978/(67.297133×0.0001)=9.804题目问一个零息债券的面值是100US期限是10年，当利率是4%，半年付息一次时，01和effective ration是多少？债券的价格V0=100/(1+4%/2)^(10*2)=67.297133当利率上升1bp到4.01%时，债券价格V+=100/(1+4.01%/2)^(10*2)=67.23119价格下降0.065944当利率下降1bp到3.99%时，债券价格V-=100/(1+3.99%/2)^(10*2)=67.36314价格上升0.06601201=（0.065944 +0.066012）= 0.065978effectiveration=0.065978/(67.297133×0.0001)=9.804 烦请写下计算步骤先谢谢。另外，零息债券久期不是到期日吗？根据57页另一个求01的公式不是同样可以求吗？当然两个结果绝对不相同。请问错误在哪里呢？

2023-03-29 17:45 2 · 回答

NO.PZ2020011303000219 问题如下 Consir a zero-coupon bonwith a favalue of US100 ana maturity of ten years. Whis the 01 anthe effective ration when the ten-yerate is 4% with semi-annucompounng? (Consir one-basis-point changes anmeasure rates cimals when calculating ration.) The value of the bonis100/1.0220=67.297133When the ten-yerate increases to 4.01%, the value creases 0.065944 to 67.231190. When the ten-yerate creases to 3.99%, the value increases 0.066012 to 67.363145. The 01 cestimatethe average of 0.065944 an0.066012, or 0.065978. The effective ration is 0.065978/(67.297133×0.0001)=9.804 这个题的ration是10，为什么mofieration不能是10/1+y呢？

2022-07-02 11:00 2 · 回答

老师您好，01的计算可以只通过crease或increase 1%的rate来计算吗？还是只能向答案中写的计算上升和下降的平均值？谢谢

2020-03-10 22:19 2 · 回答