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皓皓心 · 2024年10月20日

算法我明白，但是为什么零息债还能按半年付息

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000220

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 effective convexity of the bond when the ten-year rate is 4% with semi-annual compounding? (Consider one basis-point changes and measure rates as decimals.)

选项：

解释：

The effective convexity is

(67.231190+ 67.363145－2×67.297133)/ (67.297133×0.00012)=102.53

Note that more decimal places than those indicated were kept to provide this estimate of convexity.

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，effective convexity是多少？

effective convexity=(V+ + V- -2*V0)/(V0*1bp^2)

(67.231190+ 67.363145－2×67.297133)/ (67.297133×0.0001^2)=102.53

算法我明白，但是为什么零息债还能按半年付息

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1 个答案

李坏_品职助教 · 2024年10月20日

嗨，从没放弃的小努力你好：


semi-annual compounding的意思是，半年复利的计算方式。所以要按照半年为1个时间单位进行复利现值的计算。零息债券也是可以按照半年进行复利现值计算的。

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NO.PZ2020011303000220问题如下Consir a zero-coupon bonwith a favalue of US100 ana maturity of ten years. Whis the effective convexity of the bonwhen the ten-yerate is 4% with semi-annucompounng? (Consir one basis-point changes anmeasure rates cimals.) The effective convexity is (67.231190+ 67.363145－2×67.297133)/ (67.297133×0.00012)=102.53Note thmore cimplaces ththose incatewere kept to provi this estimate of convexity. 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，effective convexity是多少？effective convexity=(V++ V- -2*V0)/(V0*1bp^2)(67.231190+ 67.363145－2×67.297133)/(67.297133×0.0001^2)=102.53 1bp涨得到V+，1bp跌得到V-，利率一共变动了2bp，为什么除的时候用1bp呢？

2024-08-28 10:22 1 · 回答

NO.PZ2020011303000220问题如下 Consir a zero-coupon bonwith a favalue of US100 ana maturity of ten years. Whis the effective convexity of the bonwhen the ten-yerate is 4% with semi-annucompounng? (Consir one basis-point changes anmeasure rates cimals.) The effective convexity is (67.231190+ 67.363145－2×67.297133)/ (67.297133×0.00012)=102.53Note thmore cimplaces ththose incatewere kept to provi this estimate of convexity. 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，effective convexity是多少？effective convexity=(V++ V- -2*V0)/(V0*1bp^2)(67.231190+ 67.363145－2×67.297133)/(67.297133×0.0001^2)=102.53 答案中利率平方是怎么来的

2023-04-24 21:34 1 · 回答

NO.PZ2020011303000220 请问V-和V+用计算器算出来不是答案里的数啊 我是分别求的PMT=0， FV=100，I/Y=2.01 或1.99，N=20，求PV，得出来是67.43和67.165啊。 用求现值公式求出来也是这两个数。 我算的有问题么？

2021-09-07 08:32 1 · 回答

你好 请问这个价格变动的三个67是怎么得到的呢

2020-06-08 00:22 1 · 回答