Can someone explain why long interest rate call, combined with short interest rate put can have same payoff as a long position in Forward rate agreement???
In a long forward rate agreement, if the contract ends in the money i.e. the libor rate is higher than the exercise rate, then the investor gets the present value of the difference between the exercise rate and the libor rate. If the libor rate is lower than the exercise rate, then you have to pay the present value of the difference. Funds does not exchange hands at the inception of the contract. In a long interest rate call, you have an exercise price and you pay to enter the contract. If the rate at the expiry is higher then exercise rate then you earn the difference but if it is lower, it expires worthless. In a short interest rate put you receive cash since you are short. If the rate at expiry is lower than the exercise rate, then you pay the counterparty but if the rate is higher than the exercise rate, it expires worthless and you hold the cash. Now, a combination of the two contracts in the previous paragraph. You use the cash you earned in the second contract to pay for the long position in the first contract so net cash effect is zero just like the the forward rate agreement, at inception. If rate is higher than exercise rate, then you earn the difference because the first contract kicks in and the second contract expires worthless, just like forward rate agreement. If the rate is lower then exercise rate then you pay the difference and first contract expires worthless just like forward rate agreement. Hope this is helpful. Good luck.
thank you me.tega