When pricing interest rate swaps at inception, should the fixed rate or floating rate be priced first?

Question

In an interest rate swap, when pricing at inception (e.g. making sure the NPV is zero at inception), is the fixed rate set first and then the floating rate calculated (or vice-versa, e.g. floating rate set first and then the fixed rate calculated)?

I'm assuming it can be calculated both ways, so I could go to a broker and say:

I want to receive fixed 5% on $100 notional, what floating rate do I have to pay Mr Broker.

OR

I want to receive floating Libor 3M payments on $100 notional, what fixed amount do I have to pay Mr Broker.

D Stanley · Answer

The fair price for an interest rate swap is the level of the fixed coupon that sets the NPV of the swap to zero. So you would calculate the coupons based on the floating leg, then solve for the fixed coupon amount that zeros out the cash flows.

In other words, since you don't get to set the floating rate (it's set by whatever benchmark is defined in the swap contract, like SOFR) the fixed coupon is the only "knob" you can control to make the swap fair.

When pricing interest rate swaps at inception, should the fixed rate or floating rate be priced first?

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