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西红柿面 · 2024年06月15日

这道题我计算新的FRA的时候保留了更多的小数位，结果在选项里找不到

  1. CFA II
  2. Derivative

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：

A.

-US$10,625.

B.

-US$10,515.

C.

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∗(0.0316−0.0231)∗903601+0.025∗150360=US$10,515.46V_{(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.

我算的是3.1589%，然后带入公式，其他的数据和解析里面的一模一样，但是算出来是10501852，就找不到结果……………………

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李坏_品职助教 · 2024年06月16日

嗨，从没放弃的小努力你好：


对的，就是这样。-

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

李坏_品职助教 · 2024年06月15日

嗨，从没放弃的小努力你好：


首先计算新的FRA利率，

（1+1.5% / 12）^ 2 × (1+FRA新 / 12)^3 = (1+2.5%/12)^5，

所以FRA新 = 3.1671%，约等于 0.0316。

注：FRA旧 = 题目给出的条件2.31%


运用重新定价法，现在的Value of FRA = [面值5,000,000 × (FRA新 - FRA旧)×90/360] / [1+2.5%×150/360] = $10,515.46。这个求出来的是FRA多头的value。

由于本题是pay floating，也就是FRA的空头，所以最后的value是 -10,515.46

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

西红柿面 · 2024年06月16日

所以还是跟之前问的那个小数点取几位的问题一样，选个答案最接近的是吧？

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