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姜汁皮蛋 · 2022年05月11日

什么时候要考虑的t=1时间点的利息呢

NO.PZ2016082402000065

问题如下:

A bank entered into a three-year interest rate swap for a notional amount of USD 250 million, paying a fixed rate of 7.5% and receiving LIBOR annually. Just after the payment was made at the end of the first year, the continuously compounded spot one-year and two-year LIBOR rates are 8% and 8.5%, respectively. The value of the swap at that time is closest to

选项:

A.

USD 14 million

B.

USD -6 million

C.

USD -14 million

D.

USD 6 million

解释:

ANSWER: D

This question differs from the previous one, which gave the swap rate. Here, we have the spot rates for maturities of one and two years. The coupon is 7.5. The net present value (NPV) of the payments is then V=$18.75e1×8%+($250+$18.75)e2×8.5%=$244million.V=\$18.75e^{-1\times8\%}+{(\$250+\$18.75)}e^{-2\times8.5\%}=\$244million. Right after the reset, the value of the FRN is $250 million, leading to a gain of $6 million. This is a gain because the bank must pay a fixed rate but current rates are higher.

老师您好,请问这道题只用了t=2 t=3的“coupon,coupon+np”往前折现=18.75*e^-8%+(18.75+250)*e^-8.5%,却没有加上t=1时刻的18.75,这是为什么不需要加呢?那什么情况需要加上t=1时刻的利息呢。

姜汁皮蛋 · 2022年05月11日

我第二个折现忘记利率乘以2了,但是不影响我的提问。谢谢~

1 个答案

品职答疑小助手雍 · 2022年05月11日

同学你好,题目说了“ Just after the payment was made at the end of the first year, ”第一次的金额已经交换过了。

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