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lion · 2023年02月24日

请解释

NO.PZ2019052801000034

问题如下:

Assume that the annual continuously compounded spot rates are: Z1=5%,Z_1=5\%, Z2=5.1%,Z_2=5.1\%, Z3=5.2%,Z_3=5.2\%,The 1.5-year bond has a $100 face value, 6% semiannual coupon payment. Calculate the bond price:

选项:

A.

$98.34.

B.

$99.73.

C.

$100.52.

D.

$101.05.

解释:

D is correct.

考点:Interest Rate

解析:

lB=3×e[(0.05/2)×1]+3×e[(0.051/2)×2]+103×e[(0.052/2)×3]=2.93+2.85+95.27=$101.05{l}B=3\times e^{\lbrack{(-0.05/2)}\times1\rbrack}+3\times e^{\lbrack{(-0.051/2)}\times2\rbrack}+103\times e^{\lbrack{(-0.052/2)}\times3\rbrack}\\=2.93+2.85+95.27=\$101.05

说了semiannual6%.那就是半年coupon就是六为啥是三,另外我觉得公式是下面为啥错了

1 个答案

李坏_品职助教 · 2023年02月24日

嗨,从没放弃的小努力你好:


题目给的票面利息数字都是年化的,6%是一整年的票面利率,semiannual那你要6% / 2才行。这个是英语题目的习惯用语,这句话翻译过来应该是:6%年化票面利率半年计息一次的债券。


题目说了是“ annual continuously compounded”,意思是连续复利,也就是e的多少次方这种计算方法。你写的那个是离散复利,结果和连续复利比较接近,但不够精确。

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