Why is the overnight index swap rate considered a better risk-free proxy than LIBOR, and how is an OIS structured?

An overnight index swap (OIS) is an interest rate derivative where one party pays a fixed rate and receives the compounded overnight reference rate (such as SOFR, ESTR, or SONIA) over the swap's tenor. Because the floating leg resets daily at a near-risk-free overnight rate, the OIS fixed rate closely approximates the pure time value of money.\n\nOIS Mechanics:\n\nThe floating leg payment is calculated by compounding each daily overnight fixing over the accrual period:\n\nFloating payment = Notional x [Product of (1 + r_i x d_i/360) - 1]\n\nwhere r_i is the overnight rate on day i and d_i is the day count fraction (typically 1/360 for USD).\n\n`mermaid\ngraph LR\n A[\"Party A
Pays Fixed OIS Rate\"] -->|\"Fixed rate quarterly\"| B[\"Party B
Pays Compounded Overnight\"]\n B -->|\"Compounded SOFR
daily reset\"| A\n C[\"Net settlement
at period end\"] --> D[\"Only the difference
is exchanged\"]\n`\n\nWorked Example:\nFalconbridge Treasury enters a 3-month OIS with $50 million notional. The fixed rate is 4.38%. Over the 90-day period, the daily SOFR fixings compound to an effective rate of 4.42%.\n\n- Fixed leg: $50M x 4.38% x (90/360) = $547,500\n- Floating leg: $50M x 4.42% x (90/360) = $552,500\n- Net payment: Party A pays Party B $552,500 - $547,500 = $5,000\n\n(In practice, the floating leg uses exact daily compounding rather than simple interest.)\n\nWhy OIS Is a Better Risk-Free Proxy:\n\n| Feature | OIS Rate | LIBOR |\n|---|---|---|\n| Credit risk embedded | Minimal (overnight lending) | Significant (unsecured term lending) |\n| Tenor of underlying | Overnight (renewed daily) | 1M, 3M, 6M term unsecured |\n| During 2008 crisis | OIS-LIBOR spread hit 365bp | Reflected bank credit panic |\n| Counterparty exposure | Very low (daily settlement) | Higher (term exposure) |\n\nDuring the 2008 financial crisis, the spread between 3-month LIBOR and the 3-month OIS rate — known as the LIBOR-OIS spread — widened from its normal 10 basis points to over 350 basis points. This spread became the market's primary measure of banking system stress, precisely because OIS remained anchored near the true risk-free rate while LIBOR reflected panic-driven credit premiums.\n\nOIS in Derivatives Pricing:\n- Collateralized derivatives are discounted at OIS rates (because collateral earns the overnight rate)\n- The pre-crisis convention of discounting everything at LIBOR was abandoned after 2008\n- OIS discounting gives lower present values for receive-fixed swaps and higher values for pay-fixed swaps\n\nUnderstanding OIS mechanics is essential for the multi-curve framework. Dive deeper in our FRM Part I course.