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Setting the Par Fixed Rate When Pricing an Interest Rate Swap

Article Quant Q&A · Author: user1786107
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Summary

The document asks which swap leg is priced first when structuring a new interest rate swap with zero net present value at inception. It considers two equivalent ways to frame a quote: specify a desired fixed rate and ask what floating payments correspond to it, or specify the floating leg and ask for the fixed payment.

The answer explains that market dealers typically quote the fixed rate. Given the floating leg and the relevant valuation inputs, the fixed rate is selected so the swap’s value is zero at inception. Thus, in ordinary market quoting, the floating side is treated as specified and the par fixed rate is solved for. The discussion is brief and does not show the valuation equations or address conventions, curves, or other details needed to calculate an actual quote.

Key ideas

  • At inception, the par fixed rate is chosen to make the swap’s net present value zero.
  • Dealer swap quotes are generally expressed as the fixed rate.
  • The floating leg and valuation inputs provide the basis for solving for the par fixed rate.
  • Actual rate calculation depends on market conventions and valuation details not covered in the document.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# When pricing interest rate swaps at inception, should the fixed rate or floating rate be priced first?


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












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.

## Answer by siou0107 (score 3)

https://quant.stackexchange.com/a/53376

Basically, the fixed rate is the rate that SETS the value of the swap to 0. Dealers’ quotes on the swap market are quotes of the fixed rate, so it is your second way.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.