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shashankar · 2023年12月13日

题库题目

  1. FRM I
  2. Financial Markets And Products

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−R2×2=e(−R1×1−F1,2×1)e^{-R_2\times2}=e^{(-R_1\times1-F_{1,2}\times1)},or F1,2=2×3.50−1×3.25=3.75%.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×(3.75%−3.50%)×(2−1)×e−3.50%×2=2,331V=\$1,000,000\times{(3.75\%-3.50\%)}\times{(2-1)}\times e^{-3.50\%\times2}=2,331

No.PZ2016082402000058 (选择题)

来源: Handbook

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?



1、a forward rate agreement (FRA) to receive a rate of 3.75%—这句话是不是说明这个FRA的利率是3.75%且我是short position？

2、这题求t=1年时刻的value，我理解就是在t=2年时刻，用（3.75%—三个月市场的int）再折现到t=1年时刻，得出t=1年时刻的value，首先题目没有给出三个月市场的int，其次为什么value是0？

3、题目答案写的计算的远期利率是3.75%，确实没错，但是这个远期利率也不是市场利率啊，怎么能说这个利率equal to quoted rate（FRA rate）呢，不理解

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3 个答案

品职答疑小助手雍 · 2023年12月13日

3、题目计算的远期利率是3.75%，是根据1年期和2年期的zero rate算出来的理论远期利率，理论利率和公司进入的远期合约利率（quoted rate）相同，所以公司远期合约的价值为0，不会因此获利或产生损失。

品职答疑小助手雍 · 2023年12月13日

2、这题不是求的t=1时的value，而是当下t=0时的value，题目最后一句明确写了What is the value of the FRA when the deal is just entered?

同时本题的FRA出借资金的时间期限是1年，而不是3个月，你问题里写得三个月是没有来源的。

品职答疑小助手雍 · 2023年12月13日

同学你好，1、是的，long FRA是将来以固定利率borrw money。short FRA就是相当于将来要以3.75%的利率出借资金，到期收回本金和利息的合约。

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NO.PZ2016082402000058问题如下 ABInc., enterea forwarrate agreement (FRto receive a rate of 3.75% with continuous compounng on a principof US1 million between the enof ye1 anthe enof ye2. The zero rates are 3.25% an3.50% for one antwo years. Whis the value of the FRA when the is just entere A.US35,629B.US34,965C.US664US0ANSWER: he market-implieforwarrate is given e−R2×2=e(−R1×1−F1,2×1)e^{-R_2\times2}=e^{(-R_1\times1-F_{1,2}\times1)}e−R2​×2=e(−R1​×1−F1,2​×1),or F1,2=2×3.50−1×3.25=3.75%.F_{1,2}=2\times3.50-1\times3.25=3.75\%.F1,2​=2×3.50−1×3.25=3.75%. Given ththis is exactly equto the quoterate, the value must zero. If instethis rate w3.50%, for example, the value woulV=$1,000,000×(3.75%−3.50%)×(2−1)×e−3.50%×2=2,331V=\$1,000,000\times{(3.75\%-3.50\%)}\times{(2-1)}\times e^{-3.50\%\times2}=2,331V=$1,000,000×(3.75%−3.50%)×(2−1)×e−3.50%×2=2,331没看到怎么算value的（2-1）是什么东西？

2024-04-11 15:07 1 · 回答

NO.PZ2016082402000058问题如下 ABInc., enterea forwarrate agreement (FRto receive a rate of 3.75% with continuous compounng on a principof US1 million between the enof ye1 anthe enof ye2. The zero rates are 3.25% an3.50% for one antwo years. Whis the value of the FRA when the is just entere A.US35,629B.US34,965C.US664US0ANSWER: he market-implieforwarrate is given e−R2×2=e(−R1×1−F1,2×1)e^{-R_2\times2}=e^{(-R_1\times1-F_{1,2}\times1)}e−R2​×2=e(−R1​×1−F1,2​×1),or F1,2=2×3.50−1×3.25=3.75%.F_{1,2}=2\times3.50-1\times3.25=3.75\%.F1,2​=2×3.50−1×3.25=3.75%. Given ththis is exactly equto the quoterate, the value must zero. If instethis rate w3.50%, for example, the value woulV=$1,000,000×(3.75%−3.50%)×(2−1)×e−3.50%×2=2,331V=\$1,000,000\times{(3.75\%-3.50\%)}\times{(2-1)}\times e^{-3.50\%\times2}=2,331V=$1,000,000×(3.75%−3.50%)×(2−1)×e−3.50%×2=2,331抛开这个题来说，FRA计算中，long和short的计算，谁减谁这个怎么记，比如这个题的假设，3.75-3.5

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2023-07-23 19:10 1 · 回答

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