Overnight Index Swap (OIS)

An overnight index swap (OIS) is an interest rate swap that exchanges a fixed-rate payment for a floating payment based on compounded or averaged overnight benchmark rates over a defined period. The payments are calculated on a notional amount, which normally is not exchanged.

An OIS turns a sequence of daily overnight rates into one floating accrual for the payment period. It is not a loan in the overnight market, and the quoted OIS fixed rate is not the same as today’s overnight benchmark.

Key Takeaways

• The fixed leg uses a rate agreed when the swap is entered.
• The floating leg accumulates overnight benchmark observations across the contract period.
• The notional amount scales both legs but normally does not change hands.
• A pay-fixed OIS generally gains value when expected future overnight rates rise relative to the contract rate.
• OIS rates contain information about expected overnight rates, but term premia, market positioning, collateral, and other effects can also matter.
• During an accrual period, part of the floating payment may already be fixed by realized overnight observations while the remainder is still market-implied.
• SOFR, the effective federal funds rate, and the euro short-term rate are different benchmarks with different secured or unsecured market bases.
• An overnight benchmark may have less term-bank-credit content than an old interbank term rate, but an OIS contract is not literally free of market, counterparty, liquidity, or operational risk.
• Benchmark, compounding, observation dates, day count, payment lag, clearing, and collateral terms determine the actual cash flow.

How an OIS Works

Assume two parties enter a U.S. dollar OIS:

• notional amount: USD 10 million;
• fixed rate: 4.10%;
• floating benchmark: compounded SOFR;
• term: three months; and
• settlement: net cash payment at the end of the period.

The fixed-rate payer pays the fixed leg and receives the compounded overnight leg. The fixed-rate receiver does the opposite.

The exact value depends on the entire expected rate path, discounting, remaining term, settlement conventions, and collateral rather than one benchmark observation.

Floating-Leg Compounding

For each overnight observation, the contract applies the rate for the number of calendar days represented by that observation. A Friday rate may apply across a weekend under the benchmark and contract conventions.

A simplified compounded floating accrual factor is:

where (r_i) is the applicable overnight observation, (d_i) is the number of calendar days for which it applies, and (D) is the contract’s annual day-count denominator, such as 360 or 365.

The floating amount is:

The fixed amount is:

Fixed payment = notional x fixed rate x fixed-leg accrual fraction

The floating leg compounds daily rate contributions. It should not multiply an already calculated day-count fraction by another days-in-year adjustment, which would count time twice.

Actual formulas specify the rate source, publication date, observation shift, lookback, lockout, holiday treatment, day-count basis, rounding, and payment delay.

Seven-Day Compounding Example

Consider a simplified seven-day SOFR observation period. Assume Friday’s observation applies for three calendar days through the weekend and there are no lookbacks, shifts, holidays, corrections, or rounding adjustments:

Using a 360-day denominator:

The seven-day floating factor is about 0.0787729%, equivalent to an annualized simple rate of approximately 4.0512% for comparison. On USD 10 million, the floating payment is about USD 7,877.29.

If the fixed rate is 4.10%, the seven-day fixed payment is USD 7,972.22. The fixed-rate payer therefore pays about USD 94.93 net. A production calculation must use the exact benchmark calendar, observation convention, publication corrections, day count, compounding precision, and contractual rounding.

Worked Example: Net OIS Settlement

Assume the USD 10 million OIS has a 90-day period using a simplified 90/360 fixed-leg fraction.

The fixed payment at 4.10% is:

USD 10,000,000 x 4.10% x 90/360 = USD 102,500

Assume the daily overnight observations compound to a floating accrual equivalent to an annualized 4.18% for the same 90-day basis. The floating payment is:

USD 10,000,000 x 4.18% x 90/360 = USD 104,500

The pay-fixed party receives the net difference:

USD 104,500 - USD 102,500 = USD 2,000

The example uses an annualized equivalent only to make the final comparison readable. A live contract calculates the floating factor from the underlying daily observations and its exact compounding conventions.

OIS Rate vs. Overnight Rate

A three-month OIS rate does not mean today’s overnight rate will remain constant for three months. It reflects the market price of exchanging fixed interest against the future sequence of overnight observations.

Realized and Forward-Looking Portions During a Period

Once an OIS accrual period has started, daily benchmark observations divide the floating leg into two parts:

• the realized portion, which is determined from observations already published under the contract; and
• the remaining portion, which must still be projected from current market inputs.

The two portions compound together rather than simply adding:

Suppose 30 days of a 90-day period have produced a realized factor of 0.0035, while the current curve implies a remaining 60-day factor of 0.0065. The estimated full-period factor is:

That is approximately 1.002275% for the 90-day period, or 4.0091% on a simple annualized 90/360 comparison. The estimate will change as new overnight observations replace forecast inputs. This known-versus-unknown split is important when valuing, explaining, or terminating an OIS during an accrual period.

Common Overnight Benchmarks

These benchmarks are not interchangeable. A SOFR OIS and a federal-funds OIS can have basis exposure because their underlying markets and calculation methods differ.

EONIA is a legacy euro benchmark. It was discontinued on January 3, 2022 after a transition to the euro short-term rate. New educational examples should not present EONIA as the current standard euro OIS reference.

Why OIS Rates Matter

OIS markets are used to:

• hedge exposure to overnight benchmark rates;
• transfer fixed-versus-floating rate exposure;
• express views on the path of central-bank policy and overnight money-market rates;
• build portions of interest-rate curves;
• value and risk-manage collateralized derivatives under relevant conventions; and
• compare term or credit-sensitive rates with overnight-rate expectations.

The OIS curve is useful in market analysis because overnight rates are closely connected to monetary-policy implementation. It is still a market curve, not an official forecast or guaranteed path.

Hedging a Compounded Overnight-Rate Loan

Suppose a company pays compounded SOFR plus 1.25% on a USD 10 million loan and enters a matched OIS that pays 4.10% fixed and receives the same compounded SOFR exposure. Ignoring mismatches, fees, collateral costs, and credit adjustments:

Loan: compounded SOFR + 1.25%

OIS: +4.10% fixed - compounded SOFR

Combined rate: 5.35% fixed

The OIS offsets the benchmark component, not the loan itself. The borrower still owes principal and interest to its lender and separately owes or receives swap payments. A mismatch in notional, accrual dates, compounding method, spread treatment, floors, amortization, or prepayment can leave basis risk.

Reading Policy Expectations from OIS

Suppose a short-dated OIS fixed rate rises after a central-bank announcement. That can indicate that market participants now price a higher path for overnight rates over the swap period.

The inference should remain cautious. The OIS rate can also reflect:

• timing uncertainty around policy changes;
• term or risk premiums;
• hedging and positioning demand;
• balance-sheet and liquidity conditions;
• benchmark-specific basis; and
• bid-ask and market-depth effects.

An OIS forward curve therefore shows market-implied pricing under current conditions, not a promise about future central-bank decisions.

Hypothetical Policy-Path Interpretation

Assume today’s overnight benchmark is 4.75% and a six-month OIS fixed rate is 4.10%. It would be incorrect to conclude that the market predicts one 0.65 percentage-point rate cut or that the overnight rate will equal 4.10% at six months.

For a deliberately simplified illustration, suppose the first three months are priced to average 4.50%. Ignoring compounding, discounting, unequal calendar periods, and risk premiums, an equal-weight average of 4.10% over six months would imply about 3.70% for the second three months:

Many daily paths could produce the same period average. A proper interpretation uses meeting dates, exact day weights, compounding, forwards between OIS maturities, market liquidity, and possible term or risk premiums. The calculation illustrates decomposition, not a forecast.

OIS and Derivative Discounting

OIS curves became important for discounting many collateralized derivatives because cash collateral remuneration is often tied to an overnight rate. The economic principle is to align discounting with the funding or collateral rate specified by the agreement.

This does not mean one OIS curve is universally correct. Analysts must check:

• collateral currency and eligible collateral;
• interest paid on cash collateral;
• clearinghouse or credit-support terms;
• multi-currency optionality;
• initial and variation margin treatment; and
• whether the trade is collateralized, partially collateralized, or uncollateralized.

Projection and discounting can also use different curves. A term-rate cash flow can be projected from one curve and discounted under another collateral-based curve.

OIS vs. Other Rate Contracts

Contract names alone do not establish identical exposure. A three-month compounded-SOFR OIS differs from a swap referencing a forward-looking three-month term rate.

OIS Is Not Literally Risk-Free

Overnight benchmarks are often called risk-free rates or nearly risk-free rates because they generally contain less term-bank-credit exposure than historical unsecured term benchmarks. The shorthand has limits.

• SOFR is based on secured overnight Treasury financing.
• The effective federal funds rate and the euro short-term rate are based on unsecured overnight activity.
• The swap itself creates market-value, counterparty, collateral, liquidity, and operational risk.
• Longer-dated OIS rates include expectations and market pricing over time, not only one overnight exposure.

It is more accurate to identify the exact benchmark and risk being discussed than to assume every OIS cash flow is riskless.

Valuation and Sensitivity

At inception, the par OIS fixed rate is set so the present value of the fixed leg approximately equals the present value of the projected overnight leg, before transaction-specific adjustments.

For a single payment period, the net amount to the fixed-rate payer at the payment date can be expressed as:

Here, (K) is the contract fixed rate and (\alpha) is the fixed-leg accrual fraction. At inception, the par rate is chosen so the discounted expected value of the net cash flows is approximately zero under the pricing framework. After inception, realized fixings, changed forward rates, and changed discount factors create positive or negative market value.

After trade date, value changes with:

• expected future overnight rates;
• the shape of the OIS curve;
• elapsed daily fixings for the current period;
• remaining maturity and payment schedule;
• discounting and collateral terms;
• bid-ask spread and liquidity; and
• counterparty or funding adjustments where applicable.

Notional Value is only the payment scale. Duration, DV01, curve exposure, basis, and stress loss are needed to assess rate risk.

A favorable market value is a claim rather than cash already received. Collateral or variation margin can reduce unsecured exposure but can also create liquidity needs. Notional, current market value, collateral, and the next net payment are distinct measures and should be reported separately.

Risks and Common Mistakes

• Rate risk: The OIS can lose value when the expected overnight-rate path moves against the position.
• Basis risk: The OIS benchmark may not match the loan, deposit, or derivative being hedged.
• Compounding risk: Lookbacks, shifts, holidays, and rate corrections can change the floating amount.
• In-period estimation risk: Part of the accrual can be known while the remaining daily rates are still projections.
• Counterparty risk: Bilateral positive value depends on the other party’s performance.
• Collateral liquidity: Mark-to-market changes can require cash or eligible collateral quickly.
• Curve risk: Short and long OIS maturities can move differently.
• Policy-interpretation risk: Market pricing can differ from later central-bank decisions.
• Liquidity risk: Exit cost can rise in stressed or less-active maturities.
• Operational risk: Missing fixings, calendars, rounding, and payment lags can create errors.
• Legal and fallback risk: Benchmark cessation or disruption provisions control replacement calculations.

Common mistakes include using one day’s overnight rate as the whole floating leg, double-counting the day fraction, treating the OIS rate as a guaranteed policy forecast, and describing a legacy EONIA contract as current euro-market convention.

How to Evaluate an OIS

1. Identify fixed payer, floating payer, currency, notional, effective date, and maturity.
2. Confirm the exact overnight benchmark and administrator.
3. Read compounding, averaging, observation shift, lookback, lockout, and correction rules.
4. Verify day-count conventions, holiday calendar, payment lag, and rounding.
5. Recalculate the floating factor from daily observations for a sample period.
6. Distinguish current overnight rate, realized compounded rate, OIS fixed rate, and forward rate.
7. Measure DV01, curve, and benchmark-basis exposure rather than notional alone.
8. Review clearing, collateral, margin liquidity, counterparty, and closeout terms.
9. Stress-test policy-path changes, curve shifts, benchmark divergence, and early termination.
10. Obtain qualified accounting, legal, tax, and regulatory analysis where required.
11. Separate realized daily accrual, projected remaining accrual, current value, collateral, and next payment.

Authoritative Sources

• CFTC: Swaps Report Data Dictionary
• Federal Reserve Bank of New York: SOFR
• Federal Reserve Bank of New York: Reference Rate Publication and Compounding Information
• Federal Reserve Bank of New York: Effective Federal Funds Rate
• ECB: Overview of the Euro Short-Term Rate
• ECB: Transition from EONIA to the Euro Short-Term Rate
• BIS: Overnight Index Swaps and Modern Interest Rate Derivatives

This article is educational and does not recommend an OIS, benchmark, rate position, hedge, discount curve, counterparty, or trading strategy. OIS positions can create market losses, collateral calls, basis exposure, and closeout costs.

Knowledge Check

Related Terms

• Interest Rate Swap: The broader fixed-versus-floating derivative family.
• SOFR: A secured overnight U.S. dollar benchmark used by OIS contracts.
• Euro Short-Term Rate: The current euro overnight benchmark that replaced EONIA.
• Swap Rate: The fixed rate that balances a swap’s projected legs at inception.
• Forward Rate Agreement: A derivative settling a specified future interest-rate period.
• Interest Rate Futures: Standardized exchange-traded contracts linked to rate benchmarks or instruments.
• Overnight Rate: The one-day funding concept underlying overnight benchmark observations.
• Monetary Policy: The policy framework that strongly influences overnight money-market rates without making the OIS curve an official forecast.
• Basis Risk: The risk that an OIS and the exposure being hedged do not move together as expected.

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