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Weike · 2024年03月19日

为什么是减去上一个付息日的天数

  1. CFA I
  2. Fixed Income

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。

为什么是减去上一个付息日的天数不是减去下一个付息日天数

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1 个答案

吴昊_品职助教 · 2024年03月19日

嗨，爱思考的PZer你好：


accrued interest定义中：t代表的是交割日和上一个付息日之间的天数，T代表两个付息日之间的天数。

现在settlement date of 16 June 2014：交割日是6.16，距离上一个付息日4.10，两个日子之间一共66天。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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