A swap to whose underlying interest rate index (usually LIBOR) the so-called quantization techniques are applied. In other words, this swap involves the exchange of two floating rates: one is denominated in domestic currency LIBOR (say 6-month USD LIBOR) and the other is denominated in foreign currency LIBOR (6-month sterling LIBOR) plus a given spread. The payoff of this swap is defined by a floating rate associated with one currency but is settled in another currency.
This swap is also known as a differential swap, a cross index swap, or a quanto swap.
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