# payoff on a receiver swaption

The payoff on a receiver swaption is like that of a call option on a bond issued at the exercise date of the swaption, with a coupon equal to the fixed rate of the swap, and a term equal to that of the swap.

Could you dissect this statement?

Let me try it. Receiver swaption means you have the right to receive fixed and pay float at expiration of the option. Assume, the fixed rate is 6%.

A call option on the given bond means you have the right to buy the bond if its price goes above the exercise price, i.e., if its yield drops below 6%. Assume the bond is selling at par, i.e., \$100.

1. If interest rate is 7%:

With the receiver swaption, you receive 6% and pay 7%, you’d down -1%, so you don’t exercise the swaption.

With the call option, you would not exercise because the rate is above 6%…the bond is selling at a discount now (say \$97), so you can just buy it directly, it’s cheaper.

1. If interest rate is 5%:

With the receiver swaption, you would execrise the swaption and enter into the swap, receiving 6% and paying 5%, you’re up +1%.

With the call option, you would execrise the option and buy the bond at \$100 (while the bond might be selling for \$104), so that your yield is 6%, better than the 5% current yield, you’re up +1%.

I think this is correct.

If you were trying to go in for a Pay Floating, Receive Fixed Swap – when floating rates go down - the fixed rate of a swap priced at the market would be LOWER.

You would be better off going in and exercising the receiver swaption - so you will get the higher exercise rate on the swaption’s swap.

When rates go down - bond prices go up. So if you are Long a Call Option on the Bond - when rate falls - you would exercise the Call Option. – Same as above for the Receiver Swaption.

When rates go up - the Fixed Rate on the Market swap priced at current rates will be HIGHER. You would not exercise the Swaption but instead purchase a new swap at market rates. Call Option on the Bond would expire worthless.

cpk, the rest of your message is fine but the above is not clear. You already have the option to go into the swap or not. You bought a receiver swaption to receive fixed at some later date and pay float. If float rates go down, true a *newly-issued* swap will have a *lower* fixed rate as you indicated, but you already locked in the higher receive fixed rate.