For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks.
Can somebody show it how these differ from each other in an example?
The scope of this question is quite large. There are a lot of ways of hedging interest rate risk. Note that there is a quantitative finance stack exchange, and this question might fit better there.
All rates instruments have a sensitivity to interest rate changes. That is, their value goes up or down in response to interest rate movements.
If we assume that all interest rates move together in parallel (that is, spreads are unchanged), all you need to do to hedge interest rate risk is find instruments that have a value change that cancels the risk you want to hedge.
To a certain extent, most non-credit rates are correlated, and so one can use a wide variety of instruments to hedge.
However, rate movements are not perfectly correlated. As such, hedges may need to be structured to have a sensitivity closer to the risk to be hedged. How that is done is the full time job of interest rate traders. That is, too large a scope to be ansered in a single question here.
They differ in the type of Derivative Contract that is chosen.
A Swap would be an agreement with a second counterparty, in which in your example, the bank would swap or trade their interest rate asset, with a second counterparty, and which the bank would receive another asset from the second counterparty, and they agree to hold these swapped assets for a certain time stated in the swap contract. The bank may want to swap with the second counterparty, thinking that their current interest rate asset might decrease in value, so instead, they can just hold the Asset of the Counterparty, which would likely offset their current interest rate risk.
Option Contract gives the holder of the option contract, in this case, the Bank, the option to buy or sell the underlying asset at expiration, but there is no forced obligation for the Bank to buy or sell. An Option contract that moves in opposite pricing of the current interest rate risk that the Bank holds, could be chosen by the bank. Anytime during and at expiration, the bank is not obligated to, but is just given the option to either purchase or sell the underlying asset.
A Futures Contract, forces the holder of the Futures Contract, in this case the Bank to purchase the Underlying Asset at expiration. In the same scenario, a Bank could choose a Future Contract that moves in the opposite pricing of their current interest rate risk, but at the expiration time, they would be obligated to buy the current underlying asset. (the way for them to not buy the underlying asset of the futures contract is for them at some point exit and sell out of the contract before it reaches its expiration date. )
in both the Options and Futures contract case, the Bank would likely receive their hedged exposure while holding the contract before it expires.
For the Swaps Contract Case, they can be customized and crafted between the buyer and sellers of the Swap Contract, so the Bank hypothetically can customize and craft a Swap Contract that Fits their interest risk exposure as much as it can.
