折现率到DM

问题如下：

DMT Corp. issued a five-year floating-rate note (FRN) that pays a quarterly coupon of three-month market reference rate (MRR) plus 125 bps. The FRN is priced at 96 per 100 of par value. Assuming a 30/360-day count convention, evenly spaced periods, and constant three-month market reference rate (MRR) of 5%, the discount margin for the FRN is closest to:

选项：

A.180 bps.

B.221 bps.

C.400 bps.

解释：

B is correct.

(Index+QM)×FV/m = (0.05+0.0125)×100/4 =1.5625

The discount margin can be estimated by solving for DM in the equation:

The solution for the discount rate, r = (0.05 + DM)/4 is 1.8025%. Therefore, DM = 2.21% or 221 bps.

考点：浮动利率债券

解析：本题知道浮动利率债券的Reference rate和Quoted margin，也就知道分子的coupon rate。每一期的coupon=(0.05+0.0125)*100/4=1.5625，即每一期的现金流。同时，知道浮动利率债券当前的债券价格，所以可以反求出来折现率。

PV= -96，FV=100，PMT=1.5625，N=20，求得I/Y=1.8025

从而进一步求Discount margin=2.21%=221bps