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Swap Question for the Sharper Tools in the Box

Hello,
Hopefully some of you can help me understand the answer to a question I was asked in an interview. Thankfully, I pretty much guessed the right answer but the maths of it are still unknown to me. Should consult the books, I suppose...
Anyway, q goes something like:

A perfect hedge, pay Euribor, receive USD fixed.
What will be the income generated from this swap?

Answer: USD money market rate.

I guess this is to do with the FX rate interest-rate differential but if anyone can give me
a definitive answer, I would appreciate it.
It's keeping me awake at night...

Many thanks.

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