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王楚溪 · 2020年10月10日

问一道题: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,“ 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.”这句话的意思没理解,这是说第二年的libor是8%第三年的libor是8.5%吗?这不是个三年的swap吗,怎么答案里面的折现只算了两年的,题目问的“此刻”是指第一年末吗?

1 个答案

袁园_品职助教 · 2020年10月11日

同学你好!

你说的没错~ Just after the payment was made at the end of the first year 这句是在提示我们时间点,此刻就是 t=1

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