What is an Overnight Index Swap (OIS)?
An Overnight Index Swap (OIS) is an interest‑rate swap in which one counterparty pays a fixed rate and the other pays a floating rate that is tied to an overnight interest‑rate index (for example, the effective federal funds rate in the U.S., SONIA in the U.K., €STR in the euro area). The floating leg is determined by compounding the applicable overnight rates over the swap period; typically the two legs are netted and only the difference is exchanged at payment/reset dates.
Key characteristics
– Underlying: an overnight reference rate (overnight index).
– Floating calculation: compounded overnight rates over the accrual period (or the geometric average).
– Fixed leg: a single fixed interest rate agreed at trade inception.
– Settlement: usually a single net cash exchange at each reset/maturity date (or periodic resets).
– Use: hedging short‑term interest exposure, rate speculation, and discounting/valuation in collateralized markets.
How an OIS works (plain language)
– Two parties agree a notional amount and a tenor (e.g., 1 week, 3 months, 1 year).
– One party (fixed payer) agrees to pay a fixed interest rate (the OIS rate) on the notional for the period.
– The other party (floating payer) agrees to pay the compounded overnight index over the same period.
– At the payment date the two amounts are netted and the net cash flow is exchanged (often only one side pays the net).
– The floating leg is computed by compounding each day’s overnight rate over the accrual period; conventions such as day count (ACT/360, ACT/365) depend on the index and market.
Why market participants use OIS
– Hedging: protects against adverse moves in very short‑term funding costs.
– Benchmarking: the OIS curve is viewed as a close proxy for a near “risk‑free” rate in many markets and is used for discounting collateralized cash flows.
– Lower credit component: overnight rates have less term credit risk than term interbank rates (e.g., LIBOR), so OIS spreads vs. term rates reflect credit/liquidity premia.
– Trading/speculation: participants can take directional bets on short‑term rates.
Is an OIS a derivative?
Yes. An OIS is a derivative contract: its value derives from an underlying reference rate rather than ownership of an underlying asset.
How to calculate OIS payments — formulas and step‑by‑step
1) Compute the compounded floating factor for the accrual period
Let r_i be the overnight rate for calendar day i (expressed as an annual rate using the index’s day‑count convention) and d_i be the day‑count fraction for that calendar day (for daily compounding d_i is usually 1/360 or 1/365 depending on the index). For an accrual period spanning N calendar days:
Floating compound factor = ∏_{i=1..N} (1 + r_i * d_i)
Floating accrual rate for the period = Floating compound factor − 1
2) Fixed leg accrual for the same period
Fixed accrual = K * AF, where
– K = agreed fixed OIS rate (annual),
– AF = year fraction for the period using the contract day‑count convention (e.g., ACT/360).
3) Net payment at settlement (single‑payment OIS)
Net payment = Notional * (Fixed accrual − Floating accrual)
If the result is positive, the fixed‑payer receives that amount (depending on contract wording; convention varies). Typically the two legs are netted so only the net amount is exchanged.
4) Present value (if discounting is required)
To obtain present value you discount the expected net cash flow(s) using appropriate discount factors (in practice the OIS discount curve is used for collateralized trades). For a single payment at time T:
PV = DiscountFactor(0,T) * Notional * (Fixed accrual − Floating accrual)
Simple numeric example
Assumptions
– Notional = $100,000,000
– Accrual period = 30 calendar days
– Overnight rate assumed constant = 1.50% p.a. (index uses ACT/360)
– Fixed OIS rate K quoted for the 30‑day period (annualized) = 1.56% p.a.
Step A — daily day‑count fraction = 1/360. Compound factor ≈ (1 + 0.015*(1/360))^30
→ Floating compound factor ≈ (1 + 0.0000416667)^30 ≈ 1.00125
→ Floating accrual ≈ 0.00125 (0.125% for the 30‑day period)
Step B — fixed accrual = 0.0156 * (30/360) = 0.00130 (0.13% for the 30‑day period)
Step C — net payment = 100,000,000 * (0.00130 − 0.00125) = $5,000
Interpretation: the fixed leg pays slightly more than the compounded overnight floating leg; the fixed payer would receive $5,000 (net) at settlement.
Practical step‑by‑step: how a bank or treasurer would use an OIS to hedge short‑term funding exposure
1. Identify exposure: quantify the notional and the time window of short‑term rate exposure (floating borrowing or floating receivable).
2. Choose the index and tenor: select the overnight reference rate (e.g., effective federal funds, SONIA) and the swap term that matches the exposure.
3. Decide direction: if you will pay floating funding and want to lock in costs, you pay fixed and receive floating; if you receive floating and want to lock in receipts, you receive fixed.
4. Estimate required notional: size the swap to offset the rate sensitivity of the exposure (consider basis differences and any optionality).
5. Negotiate or execute the trade: on an electronic trading platform, OTC with a dealer, or cleared via a CCP. Agree day‑count, business‑day adjustments, settlement conventions and collateral terms (CSA).
6. Model cash flows: simulate the expected floating leg by compounding projected overnight rates and calculate fixed cash flows. Check break‑even and scenario outcomes.
7. Post‑trade operations: confirm trade details, set up margin/collateral arrangements, and record accounting entries (hedge‑accounting if relevant).
8. Monitor and unwind: monitor realized funding rates vs. fixed payments, manage collateral, and unwind or re‑hedge if exposures change.
Eight practical steps often cited for calculating an OIS benefit (compact form)
1. Define the exposure timeline and notional.
2. Collect historical or implied overnight rate path for the period.
3. Compute daily/day‑count fractions.
4. Compound overnight rates across the accrual period (floating factor).
5. Compute fixed leg accrual for the agreed fixed rate.
6. Subtract floating accrual from fixed accrual and multiply by notional to get net payment.
7. Discount to present value if comparing alternatives or aggregating multiple periods.
8. Compare with alternative funding/hedging costs to compute dollar benefit.
Market conventions and practical notes
– Day‑count and business‑day conventions differ by index (e.g., Fed funds often ACT/360). Use the index’s market convention.
– Many OIS trades are cleared through central counterparties (CCPs) which standardize CSA and reduce bilateral credit risk.
– In most markets OIS payments are netted and made at reset/maturity rather than daily.
– After the 2008 crisis, OIS curves became the standard for discounting collateralized derivative cash flows (“OIS discounting”) because the OIS rate closely reflects the funding/collateral rate.
Risks and limitations
– Counterparty credit risk: while lower than longer‑term unsecured interbank rates, there is counterparty risk unless cleared/fully collateralized.
– Basis risk: if the exposure is tied to a term rate (e.g., a loan indexed to a 3‑month rate), an OIS hedge introduces basis risk between the overnight index and that term rate.
– Liquidity and term mismatch: liquidity for certain tenors or indices may be limited; mismatch between exposure tenor and available OIS tenors creates imperfect hedges.
– Model/operational risk: incorrect day‑count conventions, settlement errors, or wrong compounding rules can lead to mispricing or settlement disputes.
OIS vs. LIBOR/term‑rate swaps
– OIS uses an overnight rate compounded; LIBOR swaps use a term interbank rate fixed for a period (e.g., 3M LIBOR).
– OIS typically trades at lower rates because it carries less term credit risk. The spread between term rates and OIS rose during stress periods and is an indicator of interbank stress/liquidity premia.
– Post‑LIBOR transition, markets have shifted to overnight risk‑free rates (RFRs) such as SONIA, SOFR, €STR and OIS markets play an important role in pricing and hedging.
The bottom line
An Overnight Index Swap is a widely used derivative for hedging and expressing views on short‑term interest rates. It exchanges a fixed rate for a compounded overnight floating rate and is valued and settled using index‑specific conventions. OIS contracts are central to modern interest‑rate markets — both as hedging tools and as inputs into discounting and risk management — but users must understand day‑count rules, index conventions, counterparty and basis risks.
Sources and further reading
– Investopedia — Overnight Index Swap (OIS). https://www.investopedia.com/terms/o/overnightindexswap.asp
– Cbonds — Overnight Index Swap. https://cbonds.com/terms/overnight-index-swap/
– Federal Reserve — Federal Funds Rate (for reference to the U.S. overnight index). https://www.federalreserve.gov/monetarypolicy/openmarket.htm
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.