Overnight Index Swap

An overnight index swap exchanges a fixed rate against the compounded overnight interest rate — the rate banks pay to borrow money from each other for a single night (SOFR in the US, €STR in the euro area, SONIA in the UK), which central banks steer directly.

Because the floating leg is the policy rate in all but name, an OIS is essentially a tradable bet on central bank decisions. The 6-month OIS rate tells you what the market expects the overnight rate to average over the next 6 months — cuts, hikes and all.

This is why financial news says things like "markets price a 70% chance of a cut in March": someone read it straight off the OIS curve.

Mechanics

• Floating leg: daily overnight rates compounded over the period — \(\big[\prod_d (1 + r_d \tfrac{n_d}{360}) - 1\big]\) — settled at period end.
• Fixed leg: the quoted OIS rate. For short swaps (< 1y) a single exchange at maturity; longer swaps pay periodically.
• Tiny credit content: overnight lending has minimal bank credit risk, so OIS ≈ risk-free benchmark — the reason OIS became the standard discount rate for collateralised derivatives.

Reading policy expectations

Meeting-dated OIS ("MPC-dated", "FOMC OIS") span exactly the gaps between central-bank meetings, isolating each decision. If the overnight rate is 4.00% and the OIS covering the next meeting period prices 3.92%, the market implies ~32% odds of a 25bp cut (8bp / 25bp).

OIS vs. term benchmarks

The historic LIBOR–OIS spread measured bank credit stress (its 2008 explosion was the crisis dashboard). Post-reform, most markets run on the overnight rates themselves, and OIS is the swap market's core; the surviving spreads (e.g. EURIBOR–€STR) still carry the credit-stress signal.

Valuation identity

With OIS used for both projection and discounting, floating legs collapse to discount-factor differences and the fair fixed rate is:

Bootstrapping OIS quotes therefore yields the discount curve directly — the foundation curve of every modern derivatives system, feeding CSA discounting, futures convexity and cross-currency pricing.

Extracting policy probabilities

With meeting dates \(m_k\) and piecewise-constant policy rates, the compounded OIS fixings pin down expected rates per inter-meeting period:

Caveats: this reads risk-neutral expectations — term premia and skewed scenario distributions bias the "probabilities"; sophisticated users cross-check with options on short-rate futures.

Fine structure

Actual overnight fixings drift within the policy corridor (repo supply, reserves, quarter-ends). OIS pricing embeds expected fixing spreads to the target rate; turn-of-year effects and central-bank operation changes show up as kinks. Compounding conventions (lookback, lockout, observation shift) matter operationally for payment timing.