A swap rate is the fixed rate that makes a standard swap's fixed and expected floating legs equal in present value at inception.
The swap rate is the fixed rate that makes the present value of a standard interest rate swap’s fixed leg equal to the present value of its expected floating leg at inception. It is commonly called the par swap rate because a new on-market swap is priced near zero net value before fees and transaction-specific adjustments.
A swap rate is not the current floating benchmark, a central bank’s policy rate, or the coupon on an existing swap. It is a market quote for a specified maturity and set of conventions.
Consider a plain-vanilla fixed-for-floating interest rate swap. One party pays a fixed rate and receives floating payments. The other party receives fixed and pays floating. The notional amount scales both legs but normally is not exchanged in a single-currency interest rate swap.
For a no-spread swap with floating payment dates (t_i) and fixed payment dates (T_j), a simplified par-rate formula is:
where:
The numerator is the present value of projected floating-rate payments per unit of notional. The denominator is the fixed leg’s discounted accrual factor, often called the swap annuity. Dividing one by the other gives the fixed rate that balances the two legs.
Actual valuation can require separate projection and discount curves, stub periods, compounding, payment lags, calendars, collateral currency, and other trade-specific terms. A screen rate without its conventions is incomplete.
Under a simplified single-curve framework for a spot-starting par swap with no floating spread, the floating leg can collapse to the difference between the start and maturity discount factors:
For a swap beginning today, (DF_0) is typically 1. This identity is useful for understanding the mechanics, but it should not be applied automatically to a multi-curve valuation, a seasoned swap, or a floating leg with nonstandard compounding, payment delays, or a spread.
The two curves perform different jobs:
| Curve role | Main question | Typical output |
|---|---|---|
| Projection curve | What floating coupons are implied for future reset periods? | Forward rates (F_i) |
| Discount curve | What are those future cash flows worth today? | Discount factors (DF_i) |
For a collateralized USD overnight-index swap, compounded SOFR conventions can determine the floating cash flow while collateral terms inform discounting. A different collateral currency, an uncleared trade, or a floating benchmark with another tenor can require different curves and adjustments.
“The SOFR curve” is therefore not always one universal object. A curve file should identify its instruments, market-data timestamp, interpolation, extrapolation, calendar, day counts, and collateral assumptions. Two systems can produce different swap rates from the same headline inputs if those methods differ.
Assume a simplified two-year swap with annual payments, a notional amount of USD 10 million, and the following projected rates and discount factors:
| Payment year | Projected floating rate | Discount factor | Discounted floating amount per USD 1 |
|---|---|---|---|
| 1 | 3.50% | 0.96 | 0.033600 |
| 2 | 4.10% | 0.92 | 0.037720 |
| Total | 0.071320 |
Assume each fixed-leg accrual fraction is 1.0. The discounted fixed-leg accrual factor is:
(0.96 x 1.0) + (0.92 x 1.0) = 1.88
The par swap rate is therefore:
The par rate is approximately 3.79%. On USD 10 million notional, the present value of the projected floating coupons is:
At the displayed par rate, the fixed-leg present value is:
The USD 3.20 difference is rounding from displaying the par rate with only six decimal places. Using the exact quotient makes the two present values equal.
At that fixed rate, the present values of the fixed and projected floating legs are equal under these assumptions. The undiscounted annual fixed payment would be approximately:
USD 10,000,000 x 3.7936% = USD 379,360
This is a teaching example, not a live quote. Real market calculations use full cash-flow schedules, exact day counts, curve construction methods, and contractual conventions.
Three rates are often confused:
| Rate | Meaning |
|---|---|
| Mid-market swap rate | Indicative par rate between dealer bid and offer quotes |
| Executed fixed rate | Fixed rate written into a specific swap confirmation |
| Current market swap rate | Par rate for a comparable new swap at the current valuation time |
Suppose a company entered a five-year pay-fixed swap at 4.20%. One year later, comparable remaining four-year swaps may be quoted at 3.50%. The original 4.20% contract rate does not reset. Instead, its fixed payments are now relatively high, so the position generally has negative value to the fixed payer, all else equal.
The opposite generally occurs if comparable market swap rates rise above 4.20%. Exact value still depends on the remaining payment schedule, discounting, floating reset already fixed, collateral, credit, and transaction terms.
Suppose the swap has USD 10 million notional, the company pays a contractual fixed rate of 4.20%, the current par rate for the remaining cash flows is 3.50%, and the current discounted fixed-leg accrual factor is 3.60. A first-order value to the fixed payer is:
The negative sign is consistent with paying 4.20% when a comparable new payer could pay 3.50%. This annuity approximation is not a full revaluation: it holds the current schedule and annuity fixed and omits detailed reset, curve, credit, funding, and closeout effects.
The phrase “the five-year swap rate” can hide material assumptions. Confirm:
A borrower may receive a dealer quote that differs from a public mid-market rate because the executable rate includes bid-ask spread and trade-specific economics.
Assume a company has debt priced at compounded SOFR plus 1.50%. It enters a pay-fixed, receive-SOFR swap at 3.80%. If the loan and swap use matching notionals, dates, day counts, and SOFR conventions, the simplified combined cost is:
The 3.80% swap rate does not by itself mean the company’s debt costs 3.80%. The loan spread remains, and fees, mismatched floors, payment dates, lookbacks, compounding, amortization, collateral, and early termination can prevent a perfect offset.
This is why a hedging decision should compare the debt and swap cash-flow schedules line by line rather than adding a swap to a loan based only on labels.
A swap curve plots par swap rates across maturities, such as one, two, five, ten, and thirty years. Intermediate points can be constructed from liquid market instruments under a documented curve-building method.
The curve supports several tasks:
The curve is not a list of guaranteed future short-term rates. It combines market prices, projected floating payments, discounting, liquidity, collateral conventions, and supply-demand conditions.
A curve is built from market instruments rather than observed directly at every date. Depending on currency and maturity, inputs can include overnight rates, futures, forward-rate agreements, and swaps. Calibration chooses discount factors or forward rates that reproduce those instrument prices under stated conventions.
Interpolation then fills gaps between liquid maturities. Small differences in interpolation space, instrument selection, stale-quote handling, or bootstrapping order can change forward rates and the par rate. Model governance should therefore control both the market data and the curve-building method.
| Concept | What it represents | Why it differs from a swap rate |
|---|---|---|
| Policy rate | Central bank’s administered or target rate | Usually overnight or very short term; swap rates span maturities and embed market pricing |
| SOFR | Broad measure of overnight Treasury repo financing | It can underlie a floating leg, but it is not the fixed par rate |
| Forward Rate | Rate implied for a future period | A par swap rate is a discounted average of relevant projected floating periods |
| Par Yield Curve | Coupon rates that price hypothetical bonds at par | Bond cash flows and credit or liquidity features differ from swaps |
| Government bond yield | Yield on a sovereign security | Reflects security-specific supply, liquidity, collateral, tax, and credit conditions |
| Existing swap fixed rate | Contractual rate set at execution | Does not change when current market swap rates change |
A swap spread is commonly the swap rate minus a government bond yield of comparable maturity:
Swap spread = swap rate - government bond yield
For example, if a ten-year swap rate is 4.05% and the selected ten-year government yield is 3.90%, the swap spread is positive 15 basis points. If the government yield is 4.20%, the spread is negative 15 basis points.
A negative spread is possible and is not automatically a data error. Government bond supply and demand, balance-sheet costs, secured financing conditions, pension and liability hedging, derivatives positioning, liquidity, and regulatory effects can all influence the comparison.
Do not confuse a benchmark swap spread with an asset swap spread, which comes from packaging a specific bond with a swap and depends on that bond’s price, coupon, funding, and transaction conventions.
No single observed swap rate reveals which driver dominated.
Rate risk is commonly summarized using the value change for a small movement in market rates. A position’s dollar value of one basis point, often called DV01 or PV01, estimates the price change for a one-basis-point curve move under stated assumptions.
For the two-year example, the fixed-leg annuity is 1.88 per unit of notional. Its fixed-leg PV01 is approximately:
This means a one-basis-point change in the fixed coupon changes that leg’s present value by about USD 1,880 if discount factors are held fixed. Full swap DV01 is calculated by bumping the relevant valuation curve or curves and repricing both legs; it need not equal this simple fixed-leg amount exactly.
For a pay-fixed swap:
For a receive-fixed swap, the directional relationship is generally reversed. This rule is only a first-order approximation. Curve shape changes, floating resets, optionality, basis, discounting, and large moves can produce different results.
This article is educational and does not provide a live swap quote or recommend a swap, benchmark, curve, counterparty, hedge, or trading strategy. Derivatives can create losses beyond initial cash, collateral calls, and complex closeout obligations.