How Interest-Rate Swap Valuation Algorithms Work: Fixed and Floating Legs, OIS Discounting, Forward Rates, Day Counts, DV01 and Model Checks

Quick answer: a plain-vanilla interest-rate swap exchanges interest cash flows on a notional amount without normally exchanging the notional itself. One leg pays a fixed rate; the other pays a floating rate determined from an agreed benchmark and convention. A valuation algorithm first builds the payment schedule, forecasts future floating coupons from the relevant forward curve, discounts both legs using the curve appropriate to the collateral and settlement framework, and subtracts one present value from the other. A new at-market swap has a fixed rate chosen so the two legs initially have equal value. After market rates move, the same contract develops positive value to one side and negative value to the other.

A swap notional tells you how cash flows are calculated. It does not tell you what the swap is worth.

Page role: this article owns clean interest-rate swap valuation. Yield-Curve Algorithms owns curve construction, Interest-Rate Hedges owns hedge design, and Derivatives XVA owns credit, funding, margin and capital valuation adjustments around the clean mark.

1. Start with the contract, not the market view

A valuation engine needs exact contractual terms before it needs a yield curve. For a simple fixed-for-floating swap, key inputs include:

• notional N;
• effective date and maturity;
• pay-fixed or receive-fixed direction;
• fixed coupon K;
• fixed-leg payment frequency and day-count convention;
• floating benchmark, reset frequency and compounding convention;
• business-day calendar and adjustment rule;
• payment lags, lookbacks or observation shifts where relevant;
• collateral/clearing terms that determine discounting conventions.

A one-day calendar error can change an accrual factor, payment date, discount factor and ultimately present value. Contract representation is therefore part of the mathematics, not merely data entry.

2. Fixed-leg cash flows

For fixed payment i with accrual fraction α_i:

Fixed cash flow_i = N × K × α_i.

If N = S$100 million, K = 3.20%, and the accrual fraction is 0.5, the fixed coupon is:

100,000,000 × 0.032 × 0.5 = S$1.6 million.

The present value of the fixed leg is:

PV_fixed = Σ N K α_iD(t_i)

where D(t_i) is the discount factor to payment date t_i.

3. Floating cash flows are forecast, then discounted

For future floating period j, let F_j be the forecast floating rate and β_j its accrual fraction. Then a simplified floating coupon is:

Floating cash flow_j = N × F_j × β_j.

Its present value is:

PV_float = Σ N F_jβ_jD(t_j).

The word forecast is crucial. Future floating coupons are not guessed from today’s overnight rate. They are implied by the relevant forward curve and contract convention, while already-fixed coupons use the actual fixing.

4. Swap value is the difference between two present values

For a receive-fixed swap:

PV_swap = PV_fixed − PV_float.

For a pay-fixed swap, the sign reverses.

If fixed rates rise after a receive-fixed swap was entered, its old fixed coupon becomes less attractive relative to the market and the swap generally loses value to the fixed-rate receiver. If market fixed rates fall, the old higher fixed coupon becomes more valuable.

This directional rule is a useful diagnostic, but it is not a substitute for valuation because curve shape, basis and collateral discounting also matter.

5. The par swap rate makes the initial clean PV equal to zero

For a new at-market swap, the fixed coupon K* is chosen so:

PV_fixed(K*) = PV_float.

Therefore:

K* = [Σ F_jβ_jD(t_j)] / [Σ α_iD(t_i)]

when the fixed and floating schedules are represented in the general multi-curve form.

The denominator is often called the fixed-leg annuity or PV01-related annuity term. It measures the present value of one unit of fixed coupon across the payment schedule.

6. Why modern valuation separates forecasting and discounting curves

Before the global financial crisis, simplified single-curve valuation often used one curve both to forecast floating rates and discount cash flows. Modern collateralised derivatives practice commonly separates the jobs:

• forecast curve → produces expected future benchmark fixings;
• discount curve → converts future cash flows into present value under the collateral/clearing convention.

For cleared US-dollar swaps, the industry moved to SOFR-based discounting in 2020. LCH reported transitioning more than one million contracts with roughly US$120 trillion notional to SOFR discounting, while CME separately completed its SOFR discounting transition for cleared OTC interest-rate swaps. See LCH’s transition summary and CME Clearing Advisory 20-402.

7. OIS discounting is tied to collateral economics

Why use an overnight-indexed curve for discounting? When a derivative is collateralised with daily variation margin earning an overnight rate, the economics of collateral funding affect the appropriate clean discounting framework.

For USD cleared swaps, SOFR is the central overnight secured benchmark. The New York Fed publishes SOFR, compounded averages and a SOFR Index. See New York Fed Reference Rates.

For sterling markets, the Bank of England publishes SONIA and the SONIA Compounded Index. The broader principle is not “always discount with SOFR.” It is: discounting should match the contract’s currency, collateral and clearing conventions.

8. A compact valuation example

Suppose a receive-fixed swap has notional S$100 million and two remaining annual fixed payments at 3.00%. For illustration, assume:

• D(1)=0.96;
• D(2)=0.92;
• forecast floating rates are 3.40% in year 1 and 3.60% in year 2;
• all accrual fractions are 1.0.

Fixed leg:

PV = 100m×0.03×0.96 + 100m×0.03×0.92 = S$5.64m.

Floating leg:

PV = 100m×0.034×0.96 + 100m×0.036×0.92 = S$6.576m.

Receive-fixed swap value ≈ 5.64 − 6.576 = −S$0.936m.

This is deliberately simplified to expose the mechanism. Real swaps can have more frequent payments, compounded overnight rates, stubs, payment lags and different forecast/discount curves.

9. Day counts change cash flows

“3% per year” is incomplete until the day-count convention and accrual dates are known. Common conventions include Actual/360, Actual/365 and 30/360 families.

If an accrual period has 92 actual days under Actual/360, the accrual fraction is 92/360, not exactly 0.25. On S$500 million notional, even small accrual differences can create material cash-flow differences.

A model should therefore generate the exact schedule and accrual factors from conventions instead of hard-coding “quarterly = 0.25.”

10. Business-day rules and stubs are model inputs

If a payment date falls on a weekend or holiday, contractual rules determine how it moves. Modified-following, following and preceding conventions can produce different dates. First or final periods may be short or long stubs.

A valuation mismatch between two systems often comes not from sophisticated finance but from one of these basic schedule differences:

• holiday calendar;
• business-day adjustment;
• stub placement;
• payment lag;
• reset date;
• day-count convention.

Phase-4-quality model validation therefore checks contract mechanics before blaming the yield curve.

11. Compounded overnight floating legs are path calculations

A SOFR OIS floating coupon can compound realised overnight rates across the accrual period rather than use a single term fixing. A simplified compounded factor is:

Compounded factor = Π_d(1 + r_dΔ_d) − 1.

Before the period ends, part of the coupon can already be realised while the remaining days must be forecast. The valuation engine therefore blends known fixings with forward-implied future overnight rates.

This connects to How Floating-Rate Loan Algorithms Calculate SOFR Interest, but the swap valuation problem adds two-leg present value and mark-to-market sensitivity.

12. DV01 measures local value sensitivity

DV01 is the approximate change in swap value for a one-basis-point move in the relevant rate curve.

A finite-difference calculation is:

DV01 ≈ [PV(curve − 1bp) − PV(curve + 1bp)] / 2.

Sign conventions vary, so systems should state them explicitly. A pay-fixed swap generally gains when rates rise, while a receive-fixed swap generally loses, but exact DV01 depends on remaining maturity, coupon, curve and collateral framework.

CME’s 2025 SOFR swap pricing and hedging material shows how discount factors and curve-bucket movements feed swap value and hedge quantities. See CME — Pricing and Hedging USD SOFR Interest Rate Swaps.

13. Bucketed risk catches curve-shape exposure

One parallel DV01 can hide where the sensitivity lives. A ten-year swap may have exposure across several curve nodes. A valuation engine can therefore bump individual maturities to obtain key-rate or bucketed sensitivities.

Represent the risk vector as:

d = [DV01_1Y, DV01_2Y, DV01_5Y, DV01_10Y, …].

This is the bridge from valuation to hedge construction: first measure which curve nodes own the value change; then choose offsetting instruments.

14. Clean value is not the same as all-in economic value

The calculation in this article produces a clean market value under the chosen curves and collateral framework. A bank may then add valuation adjustments for counterparty credit, own credit, funding, initial margin and capital.

Conceptually:

All-in value = clean PV +/− valuation adjustments.

The CFTC’s 2025 final amendments to swap-dealer business-conduct rules emphasise that a daily mark is an estimate and may differ from replacement or termination value; for swaps subject to daily variation margin, variation margin necessarily depends on changes in net present value. See CFTC 2025 final rule.

This is exactly why the clean valuation and XVA layers should be kept conceptually separate.

15. A robust valuation pipeline

1. Parse the legal/economic trade terms.
2. Generate exact fixed and floating schedules.
3. Load market quotes and curve inputs.
4. Build or retrieve forecast and discount curves.
5. Insert known historical fixings.
6. Forecast future floating rates.
7. Calculate fixed and floating cash flows.
8. Discount each cash flow to present value.
9. Apply pay/receive signs and net the legs.
10. Calculate DV01 and bucketed curve risk.
11. Compare with independent or simplified valuation checks.
12. Reconcile margin/clearing marks where relevant.
13. Add XVA only in the separate all-in valuation layer.
14. Revalue whenever market data, fixings or trade terms change.

16. Failure modes

• Notional=value error. The contract notional is mistaken for current exposure or market value.
• Single-curve habit. Forecasting and discounting are collapsed without checking collateral conventions.
• Wrong fixing treatment. Already-known floating rates are re-forecast.
• Day-count shortcut. Quarterly cash flows are assumed to have 0.25 accrual regardless of actual dates.
• Calendar mismatch. Two systems use different holiday or business-day rules.
• Stub blindness. Short or long initial/final periods are treated as regular coupons.
• Sign error. Pay-fixed and receive-fixed positions are valued from the wrong perspective.
• Curve-node mismatch. A parallel DV01 hides a large key-rate exposure.
• XVA contamination. Credit/funding adjustments are mixed into the clean mark and then added again elsewhere.

17. Diagnostics, alternatives and falsifiers

• Does a newly priced at-market swap have clean PV close to zero?
• Do fixed-leg cash flows reconcile exactly to notional, coupon and accrual fractions?
• Are past floating fixings identical to official benchmark data?
• Does receive-fixed value generally fall when the relevant curve is bumped upward?
• How much of PV difference between two systems comes from schedule versus curve?
• Can the result be approximated independently using par rate and annuity?
• Do bucketed DV01s sum approximately to parallel DV01 for small bumps?
• Is the discount curve consistent with the trade’s collateral/clearing treatment?

Falsifier: suppose someone claims, “A S$1 billion swap creates S$1 billion of market exposure.” A counterexample is a newly entered at-market S$1 billion swap whose clean present value is approximately zero. Notional scales the coupons; market exposure comes from the value difference between the two legs after rates move.

18. Verification and update triggers

• Reconcile trade terms against the confirmed contract.
• Validate calendars, day counts, stubs and payment lags independently.
• Compare curve construction with the canonical yield-curve engine.
• Backtest daily PV changes against realised market moves.
• Reconcile cleared marks and variation-margin movements.
• Use an independent benchmark valuation for material trades.
• Update benchmark/fallback conventions when industry definitions change.
• Revalidate after clearing-house discounting or collateral-convention changes.

Research anchors

• CME Group — Pricing and Hedging USD SOFR Interest Rate Swaps.
• LCH — transition to SOFR discounting.
• CME — cleared OTC IRS SOFR discounting transition.
• New York Fed — SOFR and compounded reference rates.
• CFTC — swap daily marks and variation-margin valuation, 2025 final rule.

The deeper lesson

Interest-rate swap valuation is disciplined bookkeeping across time. The fixed leg is known by contract. The floating leg is partly known and partly forecast. Discount factors translate future money into present money. The par rate is the fixed coupon that balances the two legs today. DV01 measures how that balance changes when the curve moves. A strong valuation algorithm therefore does not begin with a market opinion. It begins with exact dates, exact conventions and two separately valued streams of cash—and then asks whether an independent calculation can disagree with the answer.

Educational note: This article explains public derivatives mathematics. It is not trading advice, swap-pricing advice, investment advice or a valuation for any specific contract.