Swaps as Theoretical Equivalents of Other Derivatives

Interest Rate Swaps as a Series of Forward Rate Agreements
An interest rate swap can be recreated by a series of forward rate agreements (FRAs).
A difference between an interest rate swap and a series of FRAs is that the swap will have a single fixed rate, but the forward contracts will be priced at different interest rates based on the slope of the yield curve (unless, of course the yield curve is flat, then a single rate would hold for the series of FRAs).
A plain vanilla interest rate swap can be viewed as a combination of long and short positions in interest rate futures contracts, where each futures contract would have successive maturity dates.

A currency swap replicates the act of issuing fixed or floating rate debt in one currency and using the funds raised to purchase a fixed rate or floating rate bond in another currency.
An equity swap is akin to issuing one security and using the funds raised to purchase another security.

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