Overnight Index Swap (OIS)

An overnight index swap (OIS) is a financial derivative used to exchange a fixed interest payment for a floating payment tied to an overnight interest rate index (for example, the federal funds rate, ESTR, or SONIA). The floating leg compounds the prevailing overnight rates over the swap period and the two parties settle the net difference, typically in a single payment at maturity. OISs are widely used to hedge short-term interest-rate exposure and to derive near–risk-free discount curves for pricing and risk management.

How an OIS works

• Two counterparties agree on a notional amount, a fixed rate, and a swap period.
• The floating leg is calculated by compounding daily overnight rates over the period.
• The fixed leg is computed using the agreed fixed rate and the appropriate day-count convention.
• At the end of the period, the parties net the two amounts and make one payment (the party owing more pays the difference).

Key characteristics:
– Overnight rates are compounded (geometric accumulation) rather than arithmetically averaged.
– Industry practice often uses an ACT/360 or 360-day convention for daily accruals.
– Because the floating leg is based on overnight unsecured lending rates, OISs typically carry lower credit/liquidity spread than term interbank swaps and are viewed as closer to a “risk-free” measure.

Calculation — core formulas

Let:
– N = notional
– r_t = overnight rate on day t (as a decimal)
– dt = day-count fraction for day t (commonly 1/360)
– T = total year fraction for the entire period (sum of dt values)
– R_fixed = agreed fixed annual rate (decimal)

Floating leg accrual factor:
– Accrual_floating = ∏_{t=1..n} (1 + r_t * dt) − 1

Floating payment:
– Payment_floating = N * Accrual_floating

Fixed payment (simple interest over period):
– Payment_fixed = N * R_fixed * T

Net settlement (paid by fixed-payer to floating-payer if positive):
– Net = Payment_fixed − Payment_floating

Both legs are usually discounted (if valuation is required) using appropriate discount factors; in collateralized markets the OIS curve itself is often used for discounting.

Step-by-step numeric example

Notional: $1,000,000
One-day swap (T = 1/360) with:
– Overnight rate (floating) r = 0.005% = 0.00005
– Fixed rate R_fixed = 0.0053% = 0.000053

1. Compute day fraction dt = 1/360 ≈ 0.00277778
2. Floating payment ≈ N * (1 + rdt − 1) = N * rdt = 1,000,000 * 0.00005 * (1/360) ≈ $0.13889
3. Fixed payment = N * R_fixed * T = 1,000,000 * 0.000053 * (1/360) ≈ $0.14722
4. Net = $0.14722 − $0.13889 ≈ $0.00833 (fixed-payer pays ~ $0.0083)

Note: Because overnight rates and day fractions are small, single-day payments are tiny; multi-day or multi-month swaps produce economically significant amounts because of compounding and longer T.

Why institutions use OISs

• Hedging: Protect against adverse moves in short-term borrowing costs.
• Benchmarking: OIS rates serve as a proxy for near–risk-free rates and are used to construct discount curves for valuing collateralized derivatives.
• Speculation: Traders can take directional views on short-term rate movements or on the spread between OIS and term rates.
• Liquidity and credit: OIS-based pricing typically reflects lower credit risk than swaps referencing longer-term interbank offered rates.

Risks and limitations

• Counterparty risk: While lower than many term instruments, OIS still carries counterparty exposure unless centrally cleared or collateralized.
• Basis risk: The overnight index may not perfectly offset exposure tied to other reference rates or funding sources.
• Model/valuation complexity: Correctly compounding many daily rates and matching day-count conventions is required for accurate valuation.

Quick FAQs

• Is an OIS a derivative? Yes — it is a contract whose value derives from an overnight interest rate index.
• How is the floating leg calculated? By compounding the daily overnight rates for the period (geometric accumulation).
• Are OISs considered low risk? They are generally lower risk versus term interbank swaps because the floating leg is based on overnight rates, but they still have counterparty and liquidity risks.

Key takeaways

• An OIS exchanges a fixed rate for a floating rate based on compounded overnight rates and typically settles net at maturity.
• It is a core instrument for hedging short-term interest-rate exposure and for building near–risk-free discount curves.
• Accurate valuation requires compounding daily overnight rates and using consistent day-count conventions.