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It is well known that vanilla fixed for floating swaps usually have a bit of gamma, but does a floating for floating (basis) swap have any? For the sake of simplicity, let's assume that both legs of the swaps are in the same currency.

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Yes, if the two rates belong to two different currencies having different yield curves. Or in fact any two indices (bases) having different yield curves. e.g OIS vs LIBOR or LIBOR vs UST etc.

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What if the base is the same? i.e. one leg is 3M LIBOR and the second leg is 1M LIBOR (quoted as basis spread to 3M LIBOR)? Will there be a gamma in that case? –  Andrew Aug 21 '11 at 14:18
    
in general, yes - there will be gamma even then –  Akshay Aug 22 '11 at 19:30
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