Buying a delta hedged payer swaption

Question

If I/Client buy a European payer swaption, I understand that I gives me the right to pay the fixed rate at the strike level at maturity and receive a floating rate with an IRS- I expect interest rates to rise.

Is this equivalent to say that a payer swaption is a PUT swaption / option? i.e. right to sell the fixed-to-float swap (and by convention, short a fixed-to-float swap means Client pays the fixed leg / receives floating leg).

By this logic, if I trade a delta-hedged payer swaption, I would expect to be long the payer swaption, and short the underlying - i.e. short the forward fixed-to-float swap -because the delta of a PUT is negative. Is that correct and what will be the directions of the legs of the swap for the hedge?

Answer 1

It's a bit confusing to use the terms long and short when it comes to interest rate swaps (it doesn't make much sense to "buy" or "sell" a swap anyway) - particularly in the context of bonds and the inverse price/yield relationship.

Payed or received (always referring to the fixed leg) is better terminology for swaps.

Suffice it to say:

• Short bond $\equiv$ payed swap $\equiv$ make money when yields rise (prices fall)
• Long bond $\equiv$ received swap $\equiv$ make money when yields fall (prices rise)
• payer swaption $\equiv$ call on yield $\equiv$ put on price $\equiv$ put bond option
• receiver swaption $\equiv$ put on yield $\equiv$ call on price $\equiv$ call bond option

So if you're long a delta-hedged payer swaption: you're long a call on yield (put on price) and the delta-hedge is a received position on the swap ($\equiv$ long position on a bond).

Answer 2

A payer swaption can be thought of as a call on the future swaprate, and is also a put on a bond price (with coupon the swaption's fixed rate).