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Chinazdk · 2024年01月31日

问题

NO.PZ2016031001000070

问题如下:

Bond G, described in the exhibit below, is sold for settlement on 16 June 2014.

Annual Coupon 5%

Coupon Payment Frequency Semiannual

Interest Payment Dates 10 April and 10 October

Maturity Date 10 October 2016

Day Count Convention 30/360

Annual Yield-to-Maturity 4%

The accrued interest per 100 of par value for Bond G on the settlement date of 16 June 2014 is closest to:

选项:

A.

0.46.

B.

0.73.

C.

0.92.

解释:

C is correct.

The accrued interest per 100 of par value is closest to 0.92. The accrued interest is determined in the following manner: The accrued interest period is identified as66/180. The number of days between 10 April 2014 and 16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20 days remaining in April + 30 days in May +16 days in June = 66 days total). The number of days between coupon periods is assumed to be 180 days using the 30/360 day convention.

Accrued interest = tT×PMT\text{Accrued interest = }\frac tT\times PMT

where:

t = number of days from the last coupon payment to the settlement date

T = number of days in the coupon period

t/T= fraction of the coupon period that has gone by since the last payment

PMT = coupon payment per period

Accrued interest = 66180×5.002=0.92\text{Accrued interest = }\frac{66}{180}\times\frac{5.00}2\text{=}0.92

考点:accrued interest

解析:accrued interest=coupon×t/T=(5/2)×(66/180)=0.92,故选项C正确。

由于债券半年付息,所以一期的coupon是2.5。t=66,代表的是trading day和上一个付息日之间的天数,4月10号到6月16号之间是66天。T代表的就是两个付息日之间的天数,由于我们现在是30/360,所以半年天数就是180天。将上述数据代入accrued interest的公式即可。

我想再延伸下: 如果问full price是多少 怎么计算 谢谢

2 个答案
已采纳答案

吴昊_品职助教 · 2024年01月31日

嗨,爱思考的PZer你好:


未来五笔现金流折到2014.4.10的现值之和,然后再将这个数值复利到2014年6.16。103.10就是full price。

1、先算现值,PMT=2.5,FV=100,I/Y=2,N=5,计算出PV=102.36,102.36对应的时间点是4.10

2、102.36×(1+0.02)^(66/180)=103.10,这个就是6.16的full price。

3、扣减掉AI=(66/180)*(5/2)=0.92,对应的clean price=103.10-0.92=102.18


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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Chinazdk · 2024年02月01日

Clean price /或者flat price 不应该就是4月10日的折现价格吗? 为什么和用公式 full price 减掉 AI的数值不一样呢

吴昊_品职助教 · 2024年02月01日

嗨,努力学习的PZer你好:


1、4.10是一个付息日,付息日当天的价格既可以表示为clean price,也可以表示为full price。当天是没有AI的。

2、现在我们针对的是6.16,本题中算出来的AI也是加在6.16号clean price的基础上,得到6.16的full price。和4.10无关。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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