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风若如诗 · 2024年04月25日

不懂

NO.PZ2023091701000169

问题如下:

A bond portfolio manager purchased a US Treasury bondwith a settlement date of September 25. The previous coupon payment was made onMay 1, and the next coupon payment will be made on November 1. The managerapplies the actual/actual day count convention and determines that there are184 days in the coupon period, and 37 days between the settlement date and thenext coupon payment date. Additional information about the bond is providedbelow:

  • Face value: USD 100
  • Annual coupon rate: 3%
  • Dirty (cash) price of the bond on settlement date: USD 98.13
Whatis the clean (quoted) price of the bond on the settlement date of September 25?

选项:

A.

USD 95.73

B.

USD 96.93

C.USD 97.83

D.USD 99.33

解释:

B is correct.Accrued interest (ia) is computed as follows:

where t isthe number of calendar days between the last coupon date and the settlementdate, T is the number of calendar days between the last coupondate and the next coupon date. Given the information provided:

t = 184 37 = 147

and


Thus,

The clean (quoted)price of the bond is the dirty (cash) price of the bond less accrued interest:

Clean price =dirty price accrued interest = 98.1300 1.1984 = USD 96.9316

A is incorrect.This uses the annual coupon instead of the semiannual coupon to calculate theaccrued interest.

C is incorrect.This uses the days remaining to the next coupon payment date (37) instead ofthe days elapsed since the last coupon payment date (147) to calculate theaccrued interest.

D is incorrect.This adds the accrued interest to the dirty (cash) price instead of subtractingit.

这题不是很懂,咋算出来的

1 个答案

pzqa39 · 2024年04月26日

嗨,努力学习的PZer你好:


题目:一位债券投资组合经理购买了一只美国国债,其结算日期为9月25日。上次付息日为5月1日,下次付息日为11月1日。经理采用了实际/实际天数计息法,计算得出该付息期内共有184天,自结算日至下次付息日间有37天。关于该债券的其他信息如下:

面值:USD 100

年票面利率:3%

债券在结算日的含息价格(现金价格):USD 98.13

请问这只债券在9月25日的结算日的清洁(报价)价格是多少?


clean price 是指不含应计利息的债券价格。已知含息价格为98.13美元,我们需要从含息价格中减去自上次付息日至结算日之间的应计利息,以得到clean price。

自上次付息日至结算日之间的应计利息= c*t/T

t 是指上次付息日与结算日之间的日历天数 147,T 是指上次付息日与下次付息日之间的日历天数 184

C= 100* 3%/2

代入就好了 =1.1984

Clean price =dirty price − accrued interest = 98.1300 − 1.1984 = USD 96.9316

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