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Danlei · 2021年10月23日

请问一下,为何不用第二年和第三年固定利率和浮动利率计算的利息差折现求value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.

(1+0.08)*(1+f)=(1+0.085)square,可以得出f=0.09,然后第二年末net CF=(0.08-0.075)*250M,第三年末net CF=(0.09-0.075)*250M,两年的NET CF分别用0.08和0.085折现,最后得出结果。

请问老师,这个思路错在哪里?

1 个答案

李坏_品职助教 · 2021年10月24日

嗨,努力学习的PZer你好:


你的思路本身没有太大问题,但是要注意一点,这里FRN(远期利率互换),浮动端每次reset之后的value都是等于面值的。如果我们按照折现的公式去算的话,算出来浮动端的value应该略低于250,我算了一下大概是248.36 最后248.36-44得出来和答案的D项有一定出入。


做题的时候还是按照FRN浮动端价值等于面值来算比较稳妥。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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