An interest rate swap has no upfront cost to either party at inception — that is by design. The fixed rate is set so that the swap's value is exactly zero when it is traded. This rate is called the par swap rate, and working out what it should be is the core of swap pricing.
To understand how it is calculated, you need to understand two building blocks: forward rates and discount factors.
Forward Rates and the Yield Curve
The floating leg of a swap pays a rate that is reset at each fixing period. For a SONIA swap, this is compounded daily. For a SOFR swap, similarly. The market knows today what the market expects these rates to be in the future — not with certainty, but as an implied forward rate derived from the current yield curve.
If you observe today's overnight rates and longer-maturity swap rates, you can bootstrap a forward rate curve: a set of implied rates for each future period. A one-year swap whose only payment is in one year will price off the one-year forward rate. A two-year swap will price off both the one-year forward rate and the one-year forward rate one year from now (the "1y1y" forward rate). And so on across all maturities.
This bootstrapping process — taking observable market prices and deriving the implied forward rates that are consistent with them — is called curve construction. In modern markets, this is done using overnight index swap (OIS) rates, which track central bank policy rates: SONIA in sterling, SOFR in US dollars, €STR in euros.
Discount Factors
A pound received in five years is worth less than a pound today. The discount factor for a given date converts a future cash flow into its present value. If the discount factor for five years is 0.92, then £1 million receivable in five years has a present value of £920,000 today.
In the post-LIBOR world, both the projection curve (which forecasts future floating rates) and the discounting curve (which converts future cash flows to present value) are built from the same overnight risk-free rate. Before LIBOR reform, these were separate curves — LIBOR for projection, OIS for discounting — a complexity known as multi-curve pricing.
Pricing the Fixed Leg
The fixed leg of a swap pays a known cash flow every period. If the fixed rate is 4% on a £100 million notional, the fixed payments are £2 million every six months (assuming semi-annual, actual/365 day count). Each of those payments is discounted back to today using the appropriate discount factor. Sum them all up and you have the present value of the fixed leg.
Pricing the Floating Leg
The floating leg is trickier because the future cash flows are unknown at inception. But there is a useful trick: the present value of a floating-rate bond that resets at prevailing market rates is always equal to its par value at the start of each reset period. This means the present value of all the floating payments, plus the return of notional at the end, equals the notional amount at inception.
In practice, for a plain vanilla OIS-linked swap, the present value of the floating leg is simply the notional amount minus the present value of the final notional repayment (since no principal is exchanged, this is equivalent to summing the present values of the implied forward floating payments).
The Par Swap Rate
The par swap rate is the fixed rate that makes the present value of the fixed leg exactly equal the present value of the floating leg, giving the swap a zero initial value. Mathematically, it is the weighted average of the implied forward rates over the swap tenor, where the weights are the discount factors for each payment date.
For example, if the one-year SONIA forward rate is 4.50% and the two-year forward rate (for year two) is 4.20%, and the discount factors are 0.957 and 0.917 respectively, then the two-year par swap rate is approximately:
(4.50% × 0.957 + 4.20% × 0.917) / (0.957 + 0.917) ≈ 4.36%
This is a simplified illustration; actual calculation involves compounding conventions and precise day counts, but the intuition holds.
DV01: The Key Risk Metric
Once a swap is on the books, the desk needs to measure how sensitive it is to rate moves. The standard metric is DV01 — Dollar (or pound) Value of a basis point. It measures the change in the mark-to-market value of the swap if all interest rates shift by one basis point (0.01%).
A £100 million, ten-year swap has a DV01 of roughly £75,000–£85,000 per basis point, depending on the level of rates. If rates rise by 1bp, a swap where you are paying fixed loses approximately that amount; a swap where you are receiving fixed gains it. Rates desks measure their total risk in DV01 terms, broken down by tenor bucket, and hedge accordingly.
Day Count Conventions
Day count conventions determine how interest accrues between payment dates. For GBP SONIA swaps, the convention is Actual/365 Fixed — the actual number of calendar days divided by 365, regardless of whether it is a leap year. For USD SOFR swaps, it is Actual/360. EUR €STR swaps use Actual/360 as well.
The fixed leg of swaps uses different conventions: sterling fixed legs are typically Annual, Actual/365; US dollar fixed legs are typically Semi-Annual, 30/360. These differences matter when comparing swap rates across currencies and when calculating the exact cash flows at each payment date.
Bid/Offer Spread
In interbank markets, a swap dealer will quote a swap rate as a bid (the rate at which they will pay fixed, i.e., the lower rate) and an offer (the rate at which they will receive fixed, i.e., the higher rate). The difference — the bid/offer spread — is the dealer's compensation for providing liquidity and bearing risk.
For liquid tenors (2y, 5y, 10y) in major currencies, interbank bid/offer spreads can be as narrow as 0.25 basis points. For less liquid tenors or currencies, spreads can be several basis points wider. For client transactions, the dealer adds a further margin to the mid-market rate — the "all-in" client rate — which also incorporates XVA charges (CVA, FVA, MVA).