Why is a receiver swaption equal to a call? equal, please, someone, 2010

chunty

Can someone please explain to me why a receiver swaption is equal to a call?

Furthermore, if that's the case, why is a payer swaption equal to a put?

Thanks



Edited 1 time(s). Last edit at Wednesday, June 2, 2010 at 04:55AM by CFA.Rhythm.

chandsingh

Receiver swaption = receive fixed rate. You win when rates go down.

Call option on bond = receive difference between bond price and strike price. You win when rates go down.

Hence, they are equivalent in terms of interest rate sensitivity. This is no excuses material that was covered heavily in this forum last year.

NO EXCUSES

MiniMe7

thanks

excellent responses

jacksparrow

say current market interest rates = 10%

receiver swaption: option to ''enter into a swap so that you ""receive"" a fixed interest rate of , say, 10%''.

call option: option to buy a bond (which has, say, 10% coupon) at X, which is fixed.


case 1) if market interest rates decreases, say, to 8%:

your swaption: if you enter into a swap you'll be benefited.. bcs, it pays u a higher int rate compared to market. Hence, the value of your swaption increases.

your call option on bond: since mkt int rates decreases bond value increases but bcs of your call option you can still buy the bond for the old previous rate, X. Again you are benefited. Hence, the value of call option increases.

similar logic holds when market prices increases.. in which case value of both receiver swaption and call option decrease.

you can extend the same logic, with slight modifications, to put/payer-swaption combination too.

I hope it helps.

Otabek

@CFA.Rhythm

That logic is essentially same, and should work too. Only thing is, interest rate movement is the cause and the change in bond price is the result.

President1988

i just want to be sure I got this right

a receiver swaption is essentially a:

1) call (for bond prices) because when bond prices got up, interest rates go down.

The reverse:

a payer swaption is a:

1) put (for bond prices) because when bond prices go down, interest rates go up

How does that sound?

jarobi04

I just did this this morning...

Receiver swaption is an option to enter a swap as the fixed rate receiver, right. Say the 'strike' rate in the swaption is 6%. So if you excercise the swaption, you're gonna receive fixed payments based on 6% interest.

Now if at expiry of the swaption, the market swap rate is 4%, that means that by excercising the swaption and entering into the swap at the 6% rate, you're getting 2% more than other people who enter into a swap straight from the market.

Notice also that swap rates go down as interest rates go down. (just look at the formula for calculating the swap rate). So you win when swap rates (i.e. when interest rates go down).

With a put option on interest rates, you ALSO win when rates go down.

Reverse argument for why payer swaption is similar to a caplet/call on interest rates.

ningning1984

I had this exact same problem. See if this helps.

1. Receiver swaption is a put option on interest rate. It is also a call option on Bond as you have mentioned. Why?

Suppose the fixed rate that you will receive if you exercise the option is 5%. Now market interest rates go down to 3%. You are a winner here. (also see that as interest rates go down bond prices increase). So,

Interest rates go down-->Receiver swaption valuable (Hence the put on interest rate)
Bond prices go up-->Receiver swaption valuable (Hence call option on bond prices)

*Receiver swaption also similar to floorlet since both benefit as interest rates go down.