# receiver swaption equivalent to call option?

Why receiver swaption is equivalent to call option? I thought receiver swaption benefit from interest rate fall since it is receive fixed rate, so it should be equivalent to put option, is that right?

why>>> because you are buying the right to recieve floating—you benefit when rates rise.

receiver swaption is receive fixed payment not receive floating, right?

Yes, as far as I know, “receiver” means receive fixed, and “payer” means pay fixed.

What kind of call are you talking about? An interest rate call or a call on a bond? Because the call value reacts oppositely to interest rate changes.

yea ur right. Receiver swaption is receive fixed, it is similar to put option on interest rates.

The question u are referring to is probably discussing a call option on a bond. The receiver swaption is equivalent to a put option on interest rates. But it also equivalent to a call option on a bond.

Just posted this and it looks like Clark beat me to it. Disregard my post.

Thanks for the answer, so receiver swaption is equivalent to call option on bond and put option on interest rate.

Yup.

So, is this final that receiver swaption is equivalent to call option on bond and put option on interest rate. Put option on Interst rate equivalency is not mentioned in the curriculum. Plse reply bcz exam is just around the corner.

Yup.

I thought I got that but one thing is troubling me. With a call option on a bond, your upside is unlimited, just like with any other call…if teh underlying rises, your call appreciates more and more. With a receiver swaption, you have the option to get into a swap which allows you to receive 6% and pay float. If interest rates fall (similar to bond price going up above), what happens? You still receive 6% fixed, so your upside doesn’t look like it’s same as with a call.

A couple of weeks ago, I had this concept down cold like you never seen before…what happens now, i don’t know!

Careful, call option on a bond isn’t unlimited. Call option on bond is valuable when rates fall (ie, when rates fall the value of the bond rises and the call has value). So, call option on bond is limited by the zero limit on rates.

Receiver swaption = call option on bond, both benefits when rates fall. Receive = option to receive fixed when rates are below strike. As rates fall (as above) call option on bond has value.

Payer swaption = put option on bond, both benefit when rates rise. Payer gives option to pay 5% when going fixed rate is 6%. With bond, as rates rise, put option gives you the option to sell a bond worth 90 when in reality rising rates have driven the price to 85.

In addition, a put option on a rate and put option on a bond arent the same thing either.

Trouble is that receiver swaption caps your profit, but that’s not the case with a call on bond…as interest rates fall further your call on bond appreciates further…but as rates fall further (with receiver swaption) you still get paid a fixed amount, known from the onset! To me they are not the same.

You’re missing the fact that a call on a bond is capped also (which isnt the case with a stock). Value of a bond is capped when rates are at 0, and a bond is just the sum of all of its future cash flows because the discount factor is 1, just as a receiver is capped at a rate when rates fall to 0.

If interest rate is 10% and falls to 5%, with a call on bond, you’ll get the price appreciation of the bond price. With a receiver swaption, you’ll just get your already set rate of, say, 6%.

If interest rates fall further to 2%, again your a call on the bond appreciates further, but your receiver swaption still allows you to get your already set rate of 6%.

That’s what I’m talking about…unless I’m missing something, the two are not similiar at all!

If rates fall to 5%, and you have a receiver swaption with 6% fixed rate, you earn 6% - 5% = 1%

If rates fall further to 2%, and you have a receiver swaption with 6% fixed rate, you earn 6% - 2% = 4%

You still have to pay the floating rate with a receiver swaption. It’s still a swap!

receiver swaption = receive fixed rate, when market fixed rate > strike rate = call on bond price

that’s it, I fogot that you receive fixed and pay float! That’s called poor memory.

Although I think the magnitude of the gains is different, where if interest rates fall to zero, the bond may rise much more…probably.

Dreary you are missing the negative convexity of a callable bond.

Example.

interest rates fall to 3%, call at \$1,100 is exercissed. Anything above that doesn’t matter, u will just get \$1,100.

Just like a receiver swaption, rates fall to 1%, who cares, u still just get 3%.

I agree with that, a callable bond will change things dramatically, but here they are just saying the receiver swaption is equivalent to a call *option* on a bond, not a callable bond.