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曲轩宏 · 2023年08月16日

您好,可以问一下solve for DM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?

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 MRR. The current 6-month MRR 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 MRR+QM) × FV}/m={(0.012+0.005) × 100}/2=0.85

then calculate the discount rate per period :

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}

r=2.168%

Now, solve for DM:

1.2%+DM2=2.168%\frac{1.2\%+DM}2=2.168\%

DM = 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discount margin:2.168%=(1.2%+DM)/2,求得DM=3.14%,故选项B正确。

您好,可以问一下solve for DM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?

1 个答案

吴昊_品职助教 · 2023年08月17日

嗨,努力学习的PZer你好:


这道题的考点是浮动利率债券,对应PPT位置在基础班讲义P164页。

浮动利率债券的Discount rate = reference rate + required margin (or discount margin),换句话说我们求出了分母折现率之后,扣减掉reference rate,可以反求出对应的discount margin。(1.2%+DM)/2=2.168%,这个是一期的折现率。所以DM=2.168%×2-1.2%=3.136%


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