NO.PZ2018062006000069
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 par value is 100. 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 full price of this bond on 5 June 2013
选项:
A.100.00
B.103.17
C.100.39
解释:
B is correct.
The bond price at the first coupon payment date ( 5 April 2013) is:
N=5,I/Y=2.5,PMT=3,FV=100 → PV= -102.32
The number of days between 5 April 2013 and today (5 June 2013) is 60 days based on the 30/360 day count convention. Thus, the full price of the bond is:
102.32 ×(1+2.5%)60/180=103.17
考点:flat price & full price
解析:首先,我们将未来五笔现金流折现到2013.4.5,得到现值之和为102.32。N=5,PMT=3,I/Y=2.5,FV=100,求得PV=102.32
然后再将这个数值复利到2013.6.5,得到full price为103.17,故选项B正确。
本债券是一年付息两次的三年期的债券,总共有六笔现金流。
现在的时间点是2013.6.5,题干告知在两个月前已经有了第一笔coupon,发生在2013.4.5。因此可以得知,三年期的债券的期限为2012.10.5-2015.10.5.
现在是2013.6.5,未来还有五笔现金流,分别是2013.10.5;2014.4.5;2014.10.5;2015.4.5以及2015.10.5。
以上理解正确吗?