Swaptions and their Valuation

Swaption provides option holder the option to enter into a swap.
Payer vs. Receiver
Payer Swaption: The holder can enter into a swap as the fixed rate payer/floating rate receiver
Receiver Swaption: The holder can enter into a swap as the floating rate payer/fixed rate receiver.
Parties who expect the need for a swap in the future and want to lock in the swap rate now are common users of swaptions.
Swaptions provide flexibility to not enter a swap or postpone swap entry for a more desirable rate.
Interest Rate Swaptions - Payoffs and Cash Flows The holder of a payer swaption with positive value can realize this positive value in three ways (note the swaption holder will be in a situation where the floating rate received exceeds the fixed rate paid):

Exercise the swaption and enter into a pay fixed-receive floating interest rate swap; note that this strategy entails risk as interest rates could change and thus change the floating payment received.
Exercise the swaption and enter another pay floating-receive fixed interest rate swap at current rates. The income and outgoing swaps will offset and the swaption holder has created an annuity for him/herself.
The swaption holder may be able to arrange to receive a lump sum payment equal to the present value of the annuity created in approach #2.

= Max[0,FS(0,n,m) - x] ΣB0(hj)

FS(0,n,m) = Market rate on the underlying swap at swaption expiration.
X = The exercise rate that the payer would pay under swaption terms
B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption
Receiver Swaption payoff at expiration (based on $1 notional) =

= Max[0, x - FS(0,n,m)] ΣB0(hj)

FS(0,n,m) = Market rate on the underlying swap at swaption expiration.
X = The exercise rate that the receiver would receive under swaption terms
B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption

Swaption provides option holder the option to enter into a swap.
Payer vs. Receiver
Payer Swaption: The holder can enter into a swap as the fixed rate payer/floating rate receiver
Receiver Swaption: The holder can enter into a swap as the floating rate payer/fixed rate receiver.
Parties who expect the need for a swap in the future and want to lock in the swap rate now are common users of swaptions.
Swaptions provide flexibility to not enter a swap or postpone swap entry for a more desirable rate.
Interest Rate Swaptions - Payoffs and Cash Flows The holder of a payer swaption with positive value can realize this positive value in three ways (note the swaption holder will be in a situation where the floating rate received exceeds the fixed rate paid):

Exercise the swaption and enter into a pay fixed-receive floating interest rate swap; note that this strategy entails risk as interest rates could change and thus change the floating payment received.
Exercise the swaption and enter another pay floating-receive fixed interest rate swap at current rates. The income and outgoing swaps will offset and the swaption holder has created an annuity for him/herself.
The swaption holder may be able to arrange to receive a lump sum payment equal to the present value of the annuity created in approach #2.

= Max[0,FS(0,n,m) - x] ΣB0(hj)

FS(0,n,m) = Market rate on the underlying swap at swaption expiration.
X = The exercise rate that the payer would pay under swaption terms
B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption
Receiver Swaption payoff at expiration (based on $1 notional) =

= Max[0, x - FS(0,n,m)] ΣB0(hj)

FS(0,n,m) = Market rate on the underlying swap at swaption expiration.
X = The exercise rate that the receiver would receive under swaption terms
B0(hj) = Present value factor for each interest payment, based on the term structure at the expiration of the swaption