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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年07月23日

能用“forward 0时刻Value=0”作为解题思路吗？

NO.PZ2016082402000058

问题如下：

ABC, Inc., entered a forward rate agreement (FRA) to receive a rate of 3.75% with continuous compounding on a principal of USD 1 million between the end of year 1 and the end of year 2. The zero rates are 3.25% and 3.50% for one and two years. What is the value of the FRA when the deal is just entered?

选项：

A.

USD 35,629

B.

USD 34,965

C.

USD 664

D.

USD 0

解释：

ANSWER: D

The market-implied forward rate is given by $e^{-R_2\times2}=e^{(-R_1\times1-F_{1,2}\times1)}$ ,or $F_{1,2}=2\times3.50-1\times3.25=3.75\%.$ Given that this is exactly equal to the quoted rate, the value must be zero. If instead this rate was 3.50%, for example, the value would be $V=\$1,000,000\times{(3.75\%-3.50\%)}\times{(2-1)}\times e^{-3.50\%\times2}=2,331$

助教你好：

这题是收录在经典题里的，我答对了，但我是因为看见题干最后一句问的是the value of FRA when the dealer is just entered，便认为题目是在问我forward在0时刻的value，于是选D，我压根没理会题干给的远期利率和zero rate。而李老师的做法是先验证远期利率3.75%是否合理。

我的思路有问题吗？我看过往其他同学提问中都是在研究利率怎么算，可是这题明明不需要算吧？

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品职答疑小助手雍 · 2023年07月24日

同学你好，逻辑上不建议这样想。虽然假设这题算出结果不等于0会说明出题人不够严谨，但是题目毕竟针对的是考点。

所以既然给了这么些条件和假设，而且很明显题目是想往利率计算的方面考的，那就还是要算一下的。

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