问一道题：NO.PZ2018062006000081

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：

298 bps

314 bps

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%

老师问下为什么要除以2得0.85 感觉libor已经是半年的了不用再除以2了吧

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1 个答案

吴昊_品职助教 · 2020年02月03日

嗨，从没放弃的小努力你好：

考试中所有利率默认都是年化的，题目中给出的所有利率也都是年化的形式。Quoted margin=50bp、Libor=1.2%，这两个利率都是年化的形式。哪怕前面加了6-month Libor，1.2%也还是年化利率形式，所以我们要除以2得到半年的利率。

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

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NO.PZ2018062006000081 问题如下 There is a two-yeFRN with quotemargin 50 basis points anthe referenrate is 6-month MRR. The current 6-month MRR is 1.2% whiis supposeto constant for the following 2 years anthe floater is price95 per 100 of pvalue. Please calculate the scount margin for the floater assuming a 30/360 y-count convention anevenly spaceperio. A.298 bps B.314 bps C.217 bps B is correct.First we neeto calculate the interest payment eaperio{(6-month MRR+QM) × FV}/m={(0.012+0.005) × 100}/2=0.85then calculate the scount rate per perio:95=0.851+r+0.85(1+r)2+0.85(1+r)3+0.85+100(1+r)495=\frac{0.85}{1+r}+\frac{0.85}{(1+r)^2}+\frac{0.85}{(1+r)^3}+\frac{0.85+100}{(1+r)^4}95=1+r0.85+(1+r)20.85+(1+r)30.85+(1+r)40.85+100r=2.168%Now, solve for :1.2%+2=2.168%\frac{1.2\%+}2=2.168\%21.2%+=2.168% = 3.14%考点浮动利率债券解析知道浮动利率债券当前的债券价格和分子的Coupon rate，先反求出折现率，利用计算器PV= -95，FV=100，PMT=0.85，N=4，得到I/Y=2.168再利用折现率反求出scount margin2.168%=(1.2%+)/2，求得=3.14%，故B正确。您好，可以问一下solve for 的这个公式是在哪个知识点么？为什么要这么算呀而且算出来的2.168不用乘2么？

2023-08-16 21:03 1 · 回答

NO.PZ2018062006000081 问题如下 There is a two-yeFRN with quotemargin 50 basis points anthe referenrate is 6-month MRR. The current 6-month MRR is 1.2% whiis supposeto constant for the following 2 years anthe floater is price95 per 100 of pvalue. Please calculate the scount margin for the floater assuming a 30/360 y-count convention anevenly spaceperio. A.298 bps B.314 bps C.217 bps B is correct.First we neeto calculate the interest payment eaperio{(6-month MRR+QM) × FV}/m={(0.012+0.005) × 100}/2=0.85then calculate the scount rate per perio:95=0.851+r+0.85(1+r)2+0.85(1+r)3+0.85+100(1+r)495=\frac{0.85}{1+r}+\frac{0.85}{(1+r)^2}+\frac{0.85}{(1+r)^3}+\frac{0.85+100}{(1+r)^4}95=1+r0.85+(1+r)20.85+(1+r)30.85+(1+r)40.85+100r=2.168%Now, solve for :1.2%+2=2.168%\frac{1.2\%+}2=2.168\%21.2%+=2.168% = 3.14%考点浮动利率债券解析知道浮动利率债券当前的债券价格和分子的Coupon rate，先反求出折现率，利用计算器PV= -95，FV=100，PMT=0.85，N=4，得到I/Y=2.168再利用折现率反求出scount margin2.168%=(1.2%+)/2，求得=3.14%，故B正确。题目中的6-month MRR、quotemargin、scount margin，都是年化的利率吗？我理解的语境是6个月的利率。

2023-01-16 16:25 1 · 回答

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2022-12-05 09:58 1 · 回答

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2022-10-21 17:36 1 · 回答

2022-07-31 22:29 1 · 回答

问一道题：NO.PZ2018062006000081

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