OIS Discounting and Multi-Curve Frameworks

Before 2008, pricing an interest-rate swap used one curve for two different jobs: projecting what the floating leg would pay, and discounting all the cash flows back to present value. That shortcut assumed you could borrow and lend at that same curve's rate to fund the position — a reasonable approximation until banks' actual funding costs and Treasury-like rates pulled apart during the crisis. Since then, the two jobs have been split.

Why the split matters

A collateralized swap is, in effect, financed overnight — the collateral posted against it earns or costs the overnight rate. So the correct discount rate for its cash flows is the overnight rate, not the (usually higher) rate embedded in the floating index being swapped. Using the wrong discount curve doesn't just shift value a little; on a large notional book, mixing up the two curves can misvalue a swap portfolio by real money, because discounting compounds across every cash flow date.

Worked example

A swap has a single floating payment in one year, projected using the forecasting curve to be $530,000. To find its value today, discount using the 1-year OIS rate, say 4.80%:

$$PV = \frac{530{,}000}{1 + 0.0480} = 505{,}725$$

If a desk mistakenly discounted with the forecasting curve's own rate instead — say 5.20% because that curve sits higher — it would get:

$$PV = \frac{530{,}000}{1 + 0.0520} = 503{,}802$$

The difference, about $1,923 on a single cash flow, seems small, but a real swap book has thousands of cash flows across many years and counterparties; using the wrong discount curve systematically compounds that error across the whole portfolio.

What this means in practice

Multi-curve pricing is now standard infrastructure at every swaps desk: forecast each floating index off its own curve, but discount every cash flow — fixed or floating, on any index — off the same OIS curve, because that's the curve that reflects the real cost of funding the collateral behind the trade.