# Swaptions and their Valuation

• Swaption provides option holder the option to enter into a swap.

• 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):

1. 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.
2. 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.
3. 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.

### Value of an Interest Rate Swaption at Expiration

• Payer Swaption payoff at expiration (based on $1 notional) = \= 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

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