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.

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.