Why is long a receiver swaption and short a payer swaption equivalent to receive-fixed, pay-floating interest rate swap?
Why on earth, for god’s sake does this equivalence hold?
Why do we need to be long a receiver swaption as well? This doesn’t fit in. Why being short a payer swaption is not enough to emulate the receive-fixed, pay-floating interest rate swap? After all, being short a payer swaption, we are obliged to pay floating interest rate and receive fixed interest rate? Being long a receiver swaption is not necessary as it is just a right (not obligation) to enter a receive-fixed, pay-floating interest rate swap.
I hope somebody can explain this to me or else I will stuarnate!
Thanks in advance.