Why did the industry shift to OIS discounting for collateralized derivatives, and how does it differ from LIBOR discounting?

The shift to OIS (Overnight Index Swap) discounting reflects a fundamental reassessment of the risk-free rate and the economics of collateral. Before 2008, LIBOR was treated as virtually risk-free, but the crisis exposed significant credit risk embedded in interbank lending rates.\n\nThe Core Argument:\n\nWhen a derivative is collateralized under a Credit Support Annex (CSA), the collateral earns the overnight rate (Fed Funds, EONIA, or now SOFR/ESTR). The cost of funding the collateral is therefore the overnight rate, not LIBOR. Discounting at LIBOR would overstate the present value because LIBOR includes a term bank credit spread that doesn't apply to overnight-funded collateral.\n\n`mermaid\ngraph LR\n A[\"Pre-Crisis
Single LIBOR curve\"] --> B[\"LIBOR for forecasting
LIBOR for discounting\"]\n C[\"Post-Crisis
Dual-curve framework\"] --> D[\"IBOR/RFR for forecasting
OIS for discounting\"]\n B --> E[\"Assumed: LIBOR ~ risk-free\"]\n D --> F[\"Reality: OIS ~ funding cost of collateral\"]\n E -->|\"Crisis exposed\"| G[\"LIBOR-OIS spread blew out
to 365 bps in Oct 2008\"]\n G --> F\n`\n\nValuation Impact:\n\nConsider Waverly Partners holding a 5-year receiver swap with a $50 million notional and a fixed rate of 3.80%. Under LIBOR discounting (assume LIBOR = 4.10%), the PV of fixed payments uses LIBOR-derived discount factors. Under OIS discounting (OIS = 3.75%), discount factors are higher (lower rate means less discounting), increasing the PV of fixed cash flows.\n\nFixed leg annuity (LIBOR): 4.3721\nFixed leg annuity (OIS): 4.4294\n\nDifference per $1 notional: 0.0573\nOn $50M notional at 3.80% coupon: 50,000,000 x 0.038 x 0.0573 = $108,870 valuation difference.\n\nThis is not a trivial rounding error -- it represents real economic value.\n\nPractical Consequences:\n- Collateralized and uncollateralized swaps now have different valuations for the same cash flows\n- The LIBOR-OIS spread became a key risk indicator (credit stress gauge)\n- CSA terms (eligible collateral currency, rehypothecation rights) directly affect which OIS curve to use\n- Multi-currency CSAs require cheapest-to-deliver collateral optionality modeling\n\nCurrent State (Post-LIBOR Transition):\nWith LIBOR cessation, the dual-curve framework has evolved. USD swaps reference SOFR for both forecasting and discounting, simplifying back toward a single-curve framework -- but the principle of discounting at the collateral funding rate remains foundational.\n\nDive deeper into OIS discounting mechanics in our FRM Valuation and Risk Models course.