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*Baby 8 肖闲* · 2021年04月08日

请问102.32 按照公式不就是flat price 的PV 么？

  1. CFA I
  2. Fixed Income

NO.PZ2018062006000071

问题如下：

Today is 5 June 2013. A three-year semi-annual bond with a coupon rate of 6% just paid its first coupon payment. The interest payment dates are 5 April and 5 October. The yield-to-maturity equals to 5%. If day count convention is 30/360, calculate the flat price of this bond on 5 June 2013.

选项：

A.

102.17

B.

100.00

C.

100.24

解释：

A is correct.

The bond price at the first coupon payment date:

N=5，I/Y=2.5，PMT=3，FV=100 → PV= -102.32 

The number of days between 5 April 2013 (first coupon payment date) and today (5 June 2013) is 60 days based on the 30/360 day count convention.

Full price today:

102.32×（1+2.5%）60/180=103.17

Accrued Interest =100 × 3% × (60/180)=1

Flat price today:

Flat price= Full price- Accrued Interest=103.17-1=102.17

请问102.32 按照公式不就是flat price 的PV 么？这个数值是未来现金流的折现求和，所以是settlement 的时刻呀
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1 个答案

吴昊_品职助教 · 2021年04月09日

嗨，努力学习的PZer你好：


同学你好：

102.32是2013.4.5的PV，这一天是付息日，也就是说这个PV既可以看成是Flat price，也可以看成是full price，因为付息日当天没有AI，所以Flat=Full。settlement date是现在6.5，我们的思路是将4.5的full price复利到6.5，得到6.5的full price，再减去4.5到6.5这段时间的AI，就可以得到6.5的flat price了。我们之所以没有直接将未来五笔现金流折到6.5，是因为五笔现金流的时间间隔不同，后面四笔现金流时间间隔是半年，而从6.5到10.5之间并不是半年。因此现金流就不是一个年金的形式，我们就没有办法用计算器直接求PV了。因此才迂回了一下，先折到上一个付息日，再复利到6.5。

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NO.PZ2018062006000071问题如下 Toy is 5 June 2013. A three-yesemi-annubonwith a coupon rate of 6% just paiits first coupon payment. The interest payment tes are 5 April an5 October. The yielto-maturity equals to 5%. If y count convention is 30/360, calculate the flpriof this bonon 5 June 2013.A.102.17B.100.00C.100.24 A is correct.The bonprithe first coupon payment te:N=5，I/Y=2.5，PMT=3，FV=100 → PV= -102.32 The number of ys between 5 April 2013 (first coupon payment te) antoy (5 June 2013) is 60 ys baseon the 30/360 y count convention.Full pritoy:102.32×（1+2.5%）60/180=103.17AccrueInterest =100 × 3% × (60/180)=1Flpritoy:Flprice= Full price- AccrueInterest=103.17-1=102.17考点flpri full price解析flpri= full pri- accrueinterest = 103.17 - 1 = 102.17，故A正确。 n＝5时算的应该是2013.10.5日的折现价格吧，但是题目给的是2013.6.5开始的，我感觉应该折现到2016.4.5，这样N＝6，再根据具体日子数算出2013.6.5的价格，这样理解有什么问题吗

2023-07-05 14:48 1 · 回答

NO.PZ2018062006000071 问题如下 Toy is 5 June 2013. A three-yesemi-annubonwith a coupon rate of 6% just paiits first coupon payment. The interest payment tes are 5 April an5 October. The yielto-maturity equals to 5%. If y count convention is 30/360, calculate the flpriof this bonon 5 June 2013. A.102.17 B.100.00 C.100.24 A is correct.The bonprithe first coupon payment te:N=5，I/Y=2.5，PMT=3，FV=100 → PV= -102.32 The number of ys between 5 April 2013 (first coupon payment te) antoy (5 June 2013) is 60 ys baseon the 30/360 y count convention.Full pritoy:102.32×（1+2.5%）60/180=103.17AccrueInterest =100 × 3% × (60/180)=1Flpritoy:Flprice= Full price- AccrueInterest=103.17-1=102.17考点flpri full price解析flpri= full pri- accrueinterest = 103.17 - 1 = 102.17，故A正确。 为何N=5，能否画个时间线一下，谢谢

2023-02-18 06:43 1 · 回答

NO.PZ2018062006000071 问题如下 Toy is 5 June 2013. A three-yesemi-annubonwith a coupon rate of 6% just paiits first coupon payment. The interest payment tes are 5 April an5 October. The yielto-maturity equals to 5%. If y count convention is 30/360, calculate the flpriof this bonon 5 June 2013. A.102.17 B.100.00 C.100.24 A is correct.The bonprithe first coupon payment te:N=5，I/Y=2.5，PMT=3，FV=100 → PV= -102.32 The number of ys between 5 April 2013 (first coupon payment te) antoy (5 June 2013) is 60 ys baseon the 30/360 y count convention.Full pritoy:102.32×（1+2.5%）60/180=103.17AccrueInterest =100 × 3% × (60/180)=1Flpritoy:Flprice= Full price- AccrueInterest=103.17-1=102.17考点flpri full price解析flpri= full pri- accrueinterest = 103.17 - 1 = 102.17，故A正确。 有解题思路，但是 the first coupon payment te，N为什呢是 5 而不是6？

2022-10-19 23:09 1 · 回答

NO.PZ2018062006000071 相当于是第一笔现金流发生在4.5，即时间轴上的第1个点，未来现金流往前折到这里N=5，所以计算器第一笔算出来的哪个102.32的P应该是4.5时的价格，first interest payment, 不是coupon payment 啊，coupon 说的是6.5，之后的思路也是4.5价格的基础上再按复利计算6.5时刻的full price

2021-03-12 23:38 1 · 回答