The unifying theory of interest rate risk management rests upon the basis that all hedging instruments (swaps, caps, floors, collars) can be created directly or synthetically from each other.

The relationship between option contracts and swap transactions operates at an important level.

The Relationship between Option Contracts and Interest Rate Swaps

A call option can be replicated by continuously adjusting or dynamically managing a portfolio of securities on the underlying asset and cash. As the price of the asset rises, the call option equivalent portfolio would contain an increasing proportion of the assets .As the financial price of the asset decreases, the call option equivalent portfolio would reduce the holding of the assets.

More directly, options may have a direct relationship to interest rate swaps insofar as an interest rate swap can be characterized as a portfolio of purchased and sold options. Swap instruments, such as caps, floors and collars are in effect a series of option contracts.

The following will demonstrate the synthetic concept using simple mathematics.

A seller can provide an interest rate cap directly or synthetically.

Synthetically: