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忒弥斯的蒙眼布 · 2020年03月07日

我怎么算出来r=2.38%

问题如下：

There is a two-year FRN with quoted margin at 50 basis points and the reference rate is 6-month Libor. The current 6-month Libor is 1.2% which is supposed to be constant for the following 2 years and the floater is priced at 95 per 100 of par value. Please calculate the discount margin for the floater assuming a 30/360 day-count convention and evenly spaced periods.

选项：

A.

298 bps

B.

314 bps

C.

217 bps

解释：

B is correct.

First we need to calculate the interest payment each period:

{(6-month Libor+QM) × FV}/m={(0.012+0.005) × 100}/2=0.85

then calculate the discount rate per period :

$95=\frac{0.85}{1+r}+\frac{0.85}{(1+r)^2}+\frac{0.85}{(1+r)^3}+\frac{0.85+100}{(1+r)^4}$

r=2.168%

Now, solve for DM:

$\frac{1.2\%+DM}2=2.168\%$

DM = 3.14%

老师，我能算出0.85，然后式子也能列出来是一样的。输入计算器是PV=-95，FV=100.85，PMT=0.85，N=4，计算出来I/Y就是2.380321.怎么和答案中的r不一样？？我哪里输入错了吗？

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吴昊_品职助教 · 2020年03月07日

应该输入PV= -95，FV=100，PMT=0.85，N=4，得到I/Y=2.168

既然有四笔PMT，那么第四年的FV只有100.

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