MRR90-day和MRR120-day

NO.PZ2023020101000008

问题如下：

One month ago (30 days), Cline entered a pay floating 3 × 6 forward rate agreement (FRA) at a rate of 2.31% with a notional amount of US$5,000,000. At the time, the three-month MRR was 1.28% and the six-month MRR was 1.8%. Now, 30 days after entering the FRA, two-month MRR is 1.5% and the five-month MRR is 2.5%.

The current value of Cline’s FRA is closest to:

选项：

-US$10,625.

-US$10,515.

US$10,612.

解释：

FRA_(0,h,m) = FRA(0, 90, 90) = 0.0231

FRA _(g,h₋_g,m) = 0.0316

$V_{(0,90,90)}=5,000,000\ast\frac{(0.0316-0.0231)\ast\frac{90}{360}}{1+0.025\ast\frac{150}{360}}=US\$10,515.46$

Because this a pay floating FRA, V_(0.90,90) = -US$10,515.

这两个条件是不是用不上呢？

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1 个答案

李坏_品职助教 · 2025年03月03日

嗨，从没放弃的小努力你好：

是的。

本题说的是距离FRA签订日已经过去30天了，所以现在是t=30. 而FRA是在t=90到期，标的贷款是t=180到期。

所以有用的时间是90-30 = 60，以及180-30 = 150. 也就是“two-month MRR is 1.5% and the five-month MRR is 2.5%.”这两个条件是有用的。

（1+MRR60 * 60/360）*（1+新的FRA * 90/360）= (1+MRR150 * 150/360)，

(1+0.015 * 60/360)*（1+新的FRA*90/360）=(1+0.025 * 150/360)，所以新的FRA = 0.0316.

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