Interest Rate Swap (IRS): A Corporate Guide to Pricing, Valuation and Hedging [2026]

An interest rate swap lets a company convert floating-rate exposure into fixed (or vice versa) without refinancing its underlying debt. This guide explains the mechanics, the pricing formulas, and works through a single consistent numerical example so the cash flows and valuations tie together end to end.

Running example used throughout: a corporate with a USD 50,000,000 floating-rate loan, hedged with a 3-year, annual-pay interest rate swap. We keep periods annual and rates annually compounded to keep the arithmetic transparent; real-world conventions are covered in How the Floating Leg of a Swap Works.

What Is an Interest Rate Swap (IRS)?

An interest rate swap (IRS) is a bilateral over-the-counter (OTC) derivative contract in which two counterparties agree to exchange streams of interest payments on an agreed notional principal over an agreed term. In the most common form — a plain vanilla fixed-for-floating swap — one party pays a fixed rate and receives a floating rate, while the other does the opposite.

Two points define the instrument:

• The notional is never exchanged. It is only a reference amount used to size the interest payments. Only the net interest difference changes hands on each payment date.
• The two payment streams are called legs: the fixed leg and the floating leg.

In our running example, the corporate is the fixed-rate payer: it pays a fixed rate and receives a floating rate indexed to an overnight benchmark (e.g. SOFR).

An interest rate swap exchanges payments in a single currency; it should not be confused with an FX swap, which exchanges principal in two currencies, or a cross-currency swap, which combines currency and interest rate exposure in one contract.

Why Do Companies Use Interest Rate Swaps?

The core corporate objective is to convert interest rate exposure without touching the underlying loan. A company that has borrowed at a floating rate is exposed to rising rates; a swap lets it lock in a fixed cost of funds synthetically.

Typical corporate objectives:

• Certainty of cash flow — turn a variable interest expense into a predictable one for budgeting and covenant management.
• Protect margins — a business with fixed-price revenue and floating-rate debt protects its spread.
• Liability management — adjust the fixed/floating mix of the debt portfolio centrally, without renegotiating each facility.
• Match assets and liabilities — align the rate profile of debt with the rate profile of revenues or assets.

The swap sits alongside the loan. The loan still pays its lender; the swap independently exchanges fixed for floating with the swap counterparty (often a bank).

Interest Rate Swap Example: Hedging a USD 50M Floating-Rate Loan

The corporate has a USD 50m term loan paying SOFR + 1% to its lender. Management is worried that SOFR will rise over the next three years and wants budget certainty. SOFR worth 3.63% on 16th of June for reference

On 16th of June 2026, the company enters a 3-year swap with its bank:

Mechanically, on each payment date:

• The corporate receives SOFR from the bank → this offsets the SOFR it owes its lender.
• The corporate pays 3.86% fixed to the bank.
• It still pays the 1% credit margin to its lender (the swap does not touch this).

So the floating loan plus the swap = a synthetic fixed-rate loan at 4.86%. (How we arrive at the 3.86% fixed rate is derived in the pricing section below.)

How the Floating Leg of a Swap Works

The floating leg pays, each period, the notional multiplied by the realised value of the reference index for that period, adjusted by the day-count fraction:

Real swaps rarely use clean annual periods. A common USD market convention is fixed leg 30/360, annual or semi-annual, against floating leg ACT/360, quarterly (compounded SOFR). The year fraction τ in every formula above depends on the convention, and a fixed/floating frequency mismatch is normal. Always confirm: index, reset frequency, payment frequency, day count, business-day convention, and payment lag.

The defining feature: the rate for each period is not known in advance for the whole life of the swap. Each floating coupon is set ("fixed") by reference to the benchmark for that specific period. Today we only know the first coupon with certainty (or, for overnight benchmarks, we know it only once the period has fully elapsed, as explained in the ' When Is the Floating Rate Known? Term vs Overnight Benchmarks' section).

For pricing today, we cannot use the unknown future realised rates; instead we use the market's best estimate of each future rate — the forward rate, covered in the next section.

Forward Rates: How They're Derived From the Yield Curve

A forward rate is the interest rate, agreed today, that applies to a future period. It is extracted ("bootstrapped") from today's curve of zero-coupon rates / discount factors.

For a simple period from time T₁ to T₂, the forward rate f satisfies the no-arbitrage relationship between discount factors:

so

(With annual compounding and one-year periods, f = (1+z₂)² / (1+z₁) − 1 for the 1→2 year forward.)

Numerical example. Suppose today's annual zero-coupon rates are 1Y = 3.00%, 2Y = 3.40%, 3Y = 3.70%. The implied discount factors and one-year forward rates are:

So the market is implying that the floating rate, expected to be ~3.00% in Year 1, rises to ~3.80% and ~4.30% in Years 2 and 3. These three forwards are the rates we plug into the floating leg for pricing.

In practice, however, market participants do not always derive every forward rate directly from spot rates: observable market instruments, such as SOFR futures traded on CME or EURIBOR futures traded on Eurex, provide directly quoted market expectations from which the forward curve is built, subject to the appropriate adjustments, such as convexity adjustments for futures.

Is There One Forward Rate for the Entire Swap?

No. There is a different forward rate for each floating period. A 3-year annual swap has three floating coupons and therefore (at inception) three different forward rates — one per period — for instance : 3%, 3.8%, 4.3%).

A single number does summarise the swap — the par swap rate (the fixed rate that makes the swap worth zero but that is the weighted fixed equivalent of all the forwards, not itself a forward rate.

Is There a Market Rate for Each Future Period?

Yes — an implied one. The market does not quote a separate explicit price for every future period, but the yield curve implies a forward rate for each period through the bootstrapping relationship above.

Liquid instruments — overnight-index swaps, futures (e.g. SOFR futures), FRAs, and swap par rates at standard tenors — pin down the curve, and every intermediate forward is derived from it. So effectively there is a market-consistent rate for each future period, embedded in the curve rather than quoted one-by-one.

When Is the Floating Rate Known? Term vs Overnight Benchmarks

This depends on whether the benchmark is a term ("forward-looking") rate or a compounded overnight ("backward-looking") rate. This distinction became central after the LIBOR transition.

Term Benchmarks: Set in Advance (EURIBOR, HIBOR, Term SOFR)

A term benchmark such as EURIBOR (eurozone) or HIBOR (Hong Kong) is published for a full period (e.g. 3 months) at the start of that period. The coupon is therefore known at the beginning of the period and paid at the end ("set in advance, paid in arrears"). The borrower knows its rate for the upcoming period on day one.

Compounded Overnight Benchmarks: Known at Period End (SOFR, SONIA, €STR)

Risk-free overnight rates — SOFR (USD), SONIA (GBP), €STR (euro), TONA (JPY), SARON (CHF), CORRA (CAD) — are published daily, one day in arrears. The period's floating rate is the daily compounding of the overnight rate across the whole period, so it is only fully known at (or just before) the end of the period.

To leave time to compute the payment, the market uses conventions such as a payment lag (e.g. pay a few days after period end) or an observation shift / lookback (e.g. a 5-business-day lookback). Net effect: with these RFR benchmarks, the exact coupon is determined only at the end of the period, not the start.

In summary:

For pricing today, neither matters directly — we use forward rates either way. The distinction matters for operations and cash management (knowing the bill in advance vs. at period end).

Where to Find Forward Rates and Curve Data

Forward rates are not usually downloaded directly — they are implied by the published curves and liquid instruments. Trusted primary sources by currency:

For consolidated, ready-to-use curves and implied forwards, market participants typically rely on data vendors — Bloomberg (e.g. swap/curve screens), LSEG/Refinitiv, and ICE — or on the curves built by their swap counterparty bank. Always check the official administrator for the benchmark fixing itself, and a vendor or your bank for the curve / implied forwards.

Live rates and curves change continuously; verify current values from the sources above before transacting.

How to Price an Interest Rate Swap (Step by Step)

Pricing a swap means finding the fixed rate that makes the contract fair (zero value) at inception. The principle: the present value of the fixed leg equals the present value of the floating leg.

At inception this is set to zero by choosing the fixed rate appropriately. As a reminder the company is hedging USD 50M loan paying 3M Term SOFR + 1.00%, 3 years remaining with quaterly payments, by entering a pay-fixed / receive-floating swap.

Two curves are needed, and both come from one family — SOFR:

• Forward (projection) curve → built from SOFR futures. Our floating leg references 3M Term SOFR, which is forward-looking, but CME Term SOFR is itself derived from CME 3-month SOFR futures. So to project the 12 future quarterly coupons, the right input is the SOFR forward curve implied by those futures. The implied forward for each quarter is simply 100 − futures price.
• Discount curve → SOFR OIS (the risk-free / collateral curve). Discounting uses the rate your posted cash collateral earns under the CSA, which for a USD collateralised swap is SOFR (administered by the NY Fed). This is "OIS discounting." In the single-currency collateralised case the projection and discount curves are the same SOFR curve, separated only by a tiny Term-SOFR-vs-compounded-SOFR basis — so we use one SOFR curve for both and note the basis is omitted for clarity.

Step 1: Forward Rates (From the CME 3M SOFR Futures Strip)

On 15th of June 2026 we are checking on the closing rate of the 3-Month SOFR futures contracts (Jun 2026 through Mar 2029) and converting each price to a rate:

Step 2: Convexity Adjustment

The convexity adjustment is a property of the futures contract. It exists because a SOFR future is margined daily while a forward rate agreement isn't, so the futures rate is biased slightly above the true forward rate.

The correction is applied at the point where you turn a futures price into a forward rate:

Without falling into formula detail, the intuition behind convexity is that the gain when rate are falling are bigger than the loss when the rates increases with the same amount.

Let’s take a price of a 2 years zero-coupon that pay 5%:

Now let’s calculate the price when the price increase 1% et decrease 1%.

So the average price after price movement is greater than the initial price.

Volatility have a positive impact on the price.

As an example let’s take Quarter 6 :

For simplicity we don’t take into account the convexity but in the real pricing it should be taken into account.

Step 3: Discounting (Bootstrap Discount Factors Off the Same SOFR Curve)

How do you compute DF?

Annuity factor = It is simply the sum of [ τ * DF] across all twelve quarters — it's the present value of receiving 1.0 of rate per period, which is what you divide into the floating PV to get the par rate. With τ = 0.25 every quarter, it's 0.25 times the sum of the twelve discount factors.

Step 4: Computing the Swap Rate

Let’s verify if the Swap rate equal both leg.

We have $1.99 error due to rounding with the Swap rate

Reading the Curve: Should You Fix or Stay Floating?

Reminder spot rate (SOFR on 16th of June worth 3.63%)

The curve is humped: it slopes up from 3.67% to a peak of ~3.97% in mid-2027, then drifts back down to ~3.84%. Two things follow:

1. Upward front → the fixed rate sits above spot. That's why 3.86% > 3.63% spot. Locking a fixed rate on an upward-sloping curve always means paying above today's floating at the start. There's no avoiding it; it's the cost of pre-buying the expected rises.
2. The hump = the market prices hikes then a plateau/easing. This is the critical point for your client's thesis. The client expects rate increases — but the market already expects them too, out to mid-2027. Where the client and the market potentially disagree is the back end: the curve says rates top out and come back down, while the client may believe they keep climbing. If the client is right that the back end is too low, then locking 3.84–3.86% on the long quarters is cheap insurance. If the market's hump is right, the client just paid fair value for certainty.

Should You Enter the Swap?

It comes down to which of these the client is:

• A hedger who needs budget certainty, has covenants to protect, or simply can't absorb the downside if rates spike → fixing at 4.86% all-in is reasonable. They're knowingly paying ~23 bp of early carry to remove the tail. That's the textbook use case, and it's defensible.
• A view-taker who believes rates will exceed the forwards (beyond the ~3.97% peak the market prices) → fixing is an attractive positioning trade, because they lock 3.86% below where they think rates go. Right if they're right.
• Someone hoping to "beat floating" → a par swap gives no such edge, and on an upward curve they'll visibly pay more than floating for the first year. If rates instead follow the curve down off the hump, they'll regret fixing. Wrong reason to do it.

The honest read: the curve is only mildly upward and humped, not steep, so the cost of certainty here is modest (~23 bp of front carry, fair value overall). That makes fixing a relatively cheap hedge if certainty is the goal — but it also means the client isn't getting any bargain relative to the market, and if they're fixing purely on a "rates will rise" view, most of that rise is already paid for.

OIS Discounting: Which Rate Is Used and Why

The discounting rate is the overnight-indexed swap (OIS) / risk-free rate curve — for USD, the SOFR OIS curve. This is the modern standard ("OIS discounting") and applies whenever a swap is collateralised under a Credit Support Annex (CSA), because cash collateral earns the overnight rate. The discount factors should be consistent with the rate paid on the collateral.

This is not necessarily the same curve used to project the floating coupons — an approach known as multi-curve pricing.

Why we use SOFR OIS ?

Many good reasons to use SOFR OIS, first of all the Variation Margin equal the actual market value of the IRS. Variation margin can change daily, it can go from 10K, then -70K then +100K, so the collateral need by essence to be liquid, the bank cannot place your collateral for a longer tenor. It can place it daily against treasury bill or it can transfer it to another counterparty to cover its hedges, as the IRS it sold you is probably hedged on the market.

So throughout the ligetime of the contract the bank will receive and pay funding overnight. An overnight rate is consequently the most relevant rate.

Second, SOFR is a good fit because the collateral reduce and almost eliminate the credit risk, consequenstly the rate should be closed to an overnight rate with no risk = SOFR

With a daily exchange of Variation Margin,

• the change of the derivative is compensated by collateral
• Net exposure for both parties is reduced

If the bank would charge the credit spread on top of SOFR that would be asked to cover a credit exposure that the mecanism of collateral tends precisely to eliminate.

If no collateral, the value of the swap could not be 0, the bank would initially add a positive value for the swap (negative for you) that you would have to pay at the settlement of contract.

Do You Need a Zero-Coupon Curve for Swap Pricing?

Yes. A zero-coupon (spot) curve — equivalently the set of discount factors — is the foundation of all swap pricing. It is built by bootstrapping from liquid market instruments (deposits/OIS at the short end, futures in the belly, par swap rates at longer tenors).

In our example (3 years swap pricing) we have no difficulties to find liquid market instrument so we used the CME Three-Month SOFR futures contracts to derive to set of DF

It can be used for two things:

1. Projection — deriving the forward rates that estimate each floating coupon (see ' Forward Rates: How They're Derived From the Yield Curve' section). In our example we have no difficulties to find forward rate as they are available market data - CME Three-Month SOFR futures contracts
2. Discounting — converting each future cash flow into present value (see 'How to Price an Interest Rate Swap (Step by Step)' section).

Without a zero-coupon curve you cannot compute either the forwards or the discount factors, so it is the indispensable first step.

How to Value an Interest Rate Swap After Inception

After inception the swap is no longer worth zero — it gains or loses value as the curve moves. Re-valuation uses today's curve to re-project the remaining floating coupons and re-discount everything:

A convenient shortcut, valid at/near a reset date, expresses the value as the rate difference times the remaining annuity:

If current market swap rates are above the locked-in fixed rate, the fixed payer's swap is in the money (positive value); if below, it is out of the money (a liability). The next two sections show both.

Worked Example: Swap Value When Rates Rise

Assume that few days after inception the entire zero curve shifts up :

Worked Example: Swap Value When Rates Fall

Assume that few days after inception the entire zero curve shifts down :

DV01 / PV01: Measuring a Swap's Rate Sensitivity

The sensitivity of the swap to a 1 bp parallel move in rates is:

Here:

This is the headline risk figure treasury and the bank both watch.

How Much Markup Does the Bank Add to a Swap?

The fair "mid-market" par rate (3.8588% here) is the mid. A bank quotes the corporate a slightly worse rate and keeps the difference. The markup compensates for credit/counterparty risk (CVA), funding (FVA), capital, hedging costs and profit. For a creditworthy corporate on a vanilla swap it is typically a few basis points; for smaller or weaker credits it can be tens of basis points.

Example: Calculating the Bank's Markup

Suppose the bank quotes the corporate 3.95% fixed versus a mid of 3.8588**%** — a 9.12 bps markup.

The present value the bank earns from that 9.12 bp is:

So a 9.12 bp spread on a 3-year USD 50m swap is worth roughly USD 128,000 to the bank, embedded invisibly in the fixed rate the corporate pays. Larger notional or longer tenor increases this proportionally to the annuity. It is worth requesting the mid and negotiating the spread explicitly, or putting the trade out to competitive quote.

How Swaps Are Settled (Including Early Termination)

Swaps settle net in cash — the notional never moves.

• Periodic settlement: on each payment date only the difference between the fixed and floating amounts changes hands. For instance in Q6:

• Early termination / unwind: if the swap is closed out before maturity, it is cash-settled at its mark-to-market value. Using the rising-rates example above, the bank would pay the corporate ≈ USD 740,710 (rate increase) to tear up the swap (the swap is the corporate's asset). In the falling-rates scenario, the corporate would pay ≈ USD − 753 197 to exit.

Benefits of an Interest Rate Swap

• Budget certainty — converts variable interest expense into a fixed, predictable cost.
• No refinancing required — hedges the rate exposure without renegotiating the underlying loan.
• Flexible and tailored — notional, tenor, amortisation profile and payment frequency can be matched to the debt.
• Capital-light — no upfront premium for a vanilla par swap (unlike buying a cap/option).
• Liability management at portfolio level — adjust the fixed/floating mix centrally.
• Potential hedge-accounting treatment — may qualify to reduce P&L volatility (see considerations).

Risks and Considerations of Interest Rate Swaps

• Mark-to-market volatility —the swap can become a sizeable asset or liability as rates move (see ' Worked Example: Swap Value When Rates Rise' and 'Worked Example: Swap Value When Rates Fall' sections). This hits the balance sheet, and the PV01 figure in ' DV01 / PV01: Measuring a Swap's Rate Sensitivity' section shows the per-basis-point size of that swing.
• No upside participation — a fixed payer does not benefit if rates fall (see 'Worked Example: Swap Value When Rates Fall' section). A cap, though it costs a premium, would preserve the downside.
• Counterparty / credit risk — addressed via the ISDA Master Agreement, a CSA (collateral), and often central clearing (mandatory for many standardised IRS under Dodd-Frank / EMIR), which brings initial and variation margin requirements and therefore liquidity demands.
• Basis risk — if the swap's floating index does not exactly match the loan's index/reset, a residual exposure remains.
• Day-count and convention mismatches — legs often use different conventions (see conventions box); get them aligned with the loan.
• Break costs — early termination crystallises the mark-to-market, which can be a large outflow.
• Hedge accounting — qualifying for hedge accounting under IFRS 9 or US GAAP ASC 815 requires documentation and effectiveness testing; without it, fair-value changes go straight to P&L.
• xVA / pricing transparency — the quoted rate embeds CVA/FVA/margin; always benchmark against mid (see 'How Much Markup Does the Bank Add to a Swap?' section).

Who Should Use an Interest Rate Swap?

• Corporates with floating-rate debt that want fixed-cost certainty (the classic pay-fixed hedge).
• Borrowers seeking to hedge without refinancing an existing facility.
• Companies with fixed-rate revenues funding with floating-rate debt (margin protection).
• Treasuries managing a debt portfolio's fixed/floating mix dynamically, often alongside foreign exchange risk.
• Conversely, a company with fixed-rate debt expecting rates to fall might pay floating / receive fixed.

It is less suitable where the borrower wants to keep upside if rates fall (consider a cap), where notionals are too small to justify ISDA/clearing overhead, or where the underlying exposure is uncertain or short-dated.