What is the multi-curve framework, and why did the 2008 crisis force a separation between discounting and forward projection curves?

The multi-curve framework separates the yield curve used for discounting cash flows from the curve(s) used for projecting forward rates. Before 2008, a single LIBOR curve served both purposes because the LIBOR-OIS spread was negligibly small (1-2 basis points). The crisis exposed this as a dangerous simplification.\n\nWhy Single-Curve Broke Down:\n\nPre-crisis assumption: LIBOR approximates the risk-free rate, so discount at LIBOR and project forwards from LIBOR using the same curve.\n\nReality after 2008:\n- LIBOR-OIS spreads blew out to 350+ basis points\n- Different LIBOR tenors (1M, 3M, 6M) diverged significantly from each other\n- The basis swap market (exchanging 3M LIBOR for 6M LIBOR) showed spreads of 15-25 basis points\n- Using LIBOR for discounting overstated credit risk in the discount factor\n\n`mermaid\ngraph TD\n A[\"Pre-Crisis: Single Curve\"] --> B[\"One LIBOR curve for everything\"]\n B --> C[\"Discount at LIBOR\"]\n B --> D[\"Project forwards from LIBOR\"]\n \n E[\"Post-Crisis: Multi-Curve\"] --> F[\"Discounting Curve
OIS / risk-free rate\"]\n E --> G[\"Forward Projection Curve(s)
Separate curve per tenor\"]\n G --> H[\"1M Forward Curve\"]\n G --> I[\"3M Forward Curve\"]\n G --> J[\"6M Forward Curve\"]\n F --> K[\"Used to PV all cash flows
regardless of index\"]\n`\n\nMulti-Curve in Practice:\n\n1. Discounting curve: Built from OIS (SOFR) instruments — this represents the cost of funding collateral\n2. Forward curves: Separate curves for each floating rate tenor, built from tenor-specific instruments\n3. Calibration: Forward curves are bootstrapped using the OIS discount factors, not their own\n\nWorked Example:\nClearwater Derivatives prices a 2-year interest rate swap where the floating leg pays 3-month SOFR quarterly.\n\nStep 1: Build the OIS discount curve from SOFR OIS swaps\n- 1Y OIS discount factor: 0.9583\n- 2Y OIS discount factor: 0.9178\n\nStep 2: Project forward 3M SOFR rates from the 3M forward curve\n- Quarter 1 forward: 4.32%\n- Quarter 2 forward: 4.18%\n- Quarter 3 forward: 4.05%\n- Quarter 4 forward: 3.92% (and so on)\n\nStep 3: Discount all projected cash flows using OIS discount factors\n- Floating leg PV = sum of [Notional x Forward_i x DayFrac_i x DF_OIS(t_i)]\n\nStep 4: Solve for the fixed rate that makes fixed leg PV equal floating leg PV\n\nUsing single-curve (same curve for discounting and projection), the par swap rate might be 4.11%. Under multi-curve with OIS discounting, the par rate shifts to approximately 4.08% — a 3 basis point difference that compounds across large portfolios.\n\nKey Implications:\n- Swap valuations changed by billions across the industry when OIS discounting was adopted\n- CSA terms (what rate collateral earns) directly affect which discount curve to use\n- Cross-currency swaps require even more curves (one per currency per tenor)\n\nMaster the multi-curve framework in our FRM Part I course.