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papher · 2020年06月14日

问一道题: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 eR2×2=e(R1×1F1,2×1)e^{-R_2\times2}=e^{(-R_1\times1-F_{1,2}\times1)},or F1,2=2×3.501×3.25=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%)×(21)×e3.50%×2=2,331V=\$1,000,000\times{(3.75\%-3.50\%)}\times{(2-1)}\times e^{-3.50\%\times2}=2,331

请问答案中举的3.5%的例子在计算第2年年末的利差时(3.75%-3.5%),为什么不用e^3.75%-e^3.5%,条件不是说用连续复利吗?

1 个答案

品职答疑小助手雍 · 2020年06月15日

emmm早期frm出题人脑子比较飘(这题2016年或更早的)。。。FRA的利差计算本身按libor就是要单利做加减的,不过折现的话可以用连续复利。

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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?

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