With an interest rate swap, one party receives payments based on a fixed rate while the other party receives payments based on a floating rate (fixed-for-floating). But you could also have a swap where both parties exchange payments based on floating rates (floating-for-floating). This is called a basis swap.
Why would two parties exchange cash flows that are both based on floating rates?
To reduce interest rate basis risk. This occurs when cash flows are affected by different factors that are not perfectly correlated (an example would be floating-rate assets and floating-rate liabilities that are based on different indexes).
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