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hanfei · 2023年09月21日

how to calculate the 18.75?

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.

how to calculate the 18.75?

2 个答案

李坏_品职助教 · 2023年09月21日

嗨,爱思考的PZer你好:


题目开头说了paying a fixed rate of 7.5% and receiving LIBOR annually,意思是支付固定利率7.5%并且收取LIBOR浮动利率。


利率互换里,计算value的时候,都是要加上最后的本金,也就是说要把payment看做一个债券,支付了coupon+本金,这样才可以去和浮动利率端的250million做比较。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

李坏_品职助教 · 2023年09月21日

嗨,努力学习的PZer你好:


18.75是支付出去的coupon。18.75=250*7.5%. 答案的那个V计算的是net present value of payments,包括两笔coupon和最后的本金。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

hanfei · 2023年09月21日

怎么判断最后的本金是收到的还是付出的呢? 从答案里面判断是付出coupon+250million的本金,这是如何判断的呢

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