OIS Discounting and the Multi-Curve Framework

Every swap-valuation formula in this module has quietly leaned on one ingredient: a discount curve, used to turn a future cash flow into today's dollars. For decades, the market's answer to "which curve?" was simple to the point of being invisible — use LIBOR. LIBOR was the rate used to set a swap's floating payments, and it was also used to discount every cash flow on both legs, fixed and floating alike. One curve did both jobs. Then 2008 happened, and the industry discovered that "simple" and "correct" had quietly stopped being the same thing.

Why LIBOR looked like a free stand-in for "risk-free"

LIBOR (the London Interbank Offered Rate) was a survey-based estimate of the rate at which large, highly-rated banks could borrow unsecured from each other for a few months at a time. It was never literally risk-free — lending unsecured to a bank always carries some chance the bank doesn't pay it back — but for most of LIBOR's history that credit risk was small and stable, so quants and traders treated LIBOR as a convenient, liquid proxy for the risk-free rate. That convenience compounded: because the same panel banks whose borrowing set LIBOR were also the ones running swap desks and posting collateral on their trades, discounting a swap's cash flows at LIBOR felt like discounting at the very rate the market itself was implicitly using.

Recall from the previous lesson that LIBOR is, by construction, an interbank rate — it measures how cheaply banks lend to other banks. That's precisely why it embeds bank credit risk: it's the price of unsecured exposure to the banking sector itself. Using it as a stand-in for "risk-free" was always a convenient approximation, not a fact of nature, and approximations tend to fail precisely when the thing they're approximating over stops behaving normally — which is exactly what bank credit risk did in the autumn of 2008.

The spread that broke the approximation

The cleanest way to see LIBOR's hidden credit-risk content is the LIBOR–OIS spread: the gap between LIBOR and the overnight indexed swap (OIS) rate — a rate built from the actual overnight rate central banks target (Fed Funds in the US, now SOFR-based), which carries essentially no bank credit risk because it's secured, overnight exposure rather than unsecured, months-long lending. In ordinary times the two rates track each other closely:

Period Typical LIBOR–OIS spread
Early-to-mid 2007 (pre-crisis normal) ~10 basis points
August 2007 (first credit tremors) ~40 basis points
October 2008 (post-Lehman peak) ~350+ basis points
2010s (new normal) ~20–30 basis points

A spread that quietly sat near 10 basis points for years suddenly widened thirty-fold. Banks stopped trusting each other's solvency, unsecured interbank lending nearly seized up, and LIBOR — still being surveyed and published every day — was now visibly pricing in real, substantial bank credit risk. The market's cheap proxy for "risk-free" had stopped being anywhere close to risk-free, exactly when everyone most needed their discount curve to be trustworthy.

Why the fix is OIS, specifically

The decisive, practical reason discounting shifted to OIS is collateral. Most swaps today trade under a Credit Support Annex, and cash collateral posted against a swap's mark-to-market value typically earns interest at the overnight rate — OIS — not at LIBOR. That makes OIS the actual rate at which money can be borrowed or lent against a collateralized swap position, which is precisely the rate a discounted-cash-flow valuation is supposed to use. Discounting collateralized cash flows at LIBOR was, in hindsight, discounting at the wrong rate for the economics that were actually in force.

Worked example. A collateralized swap has a single remaining cash flow of \$10{,}000{,}000 due in five years. Discount it at a flat LIBOR of 4.50\% versus a flat OIS of 4.20\% (continuously compounded):

\text{PV}_{\text{LIBOR}} = 10{,}000{,}000\,e^{-0.045 \times 5} \approx \$7{,}985{,}200, \text{PV}_{\text{OIS}} = 10{,}000{,}000\,e^{-0.042 \times 5} \approx \$8{,}105{,}800.

A gap of roughly \$120{,}600 — about 1.5% of the payment's value — from switching discount curves on a single cash flow. Multiply that kind of gap across every cash flow on every swap in a dealer's book, which can easily run into hundreds of billions of dollars of notional, and "which curve to discount with" stops being a rounding footnote and becomes a genuine, multi-million-dollar valuation question — exactly why the whole market moved in the same direction at once.

See the two curves diverge

Two discount-factor curves, e^{-rt} for each flat rate, plotted against maturity. The higher-rate curve (LIBOR) discounts more aggressively — its factors sit below the OIS curve's at every maturity beyond zero, and the gap between them widens the further out you look, exactly matching the growing dollar gap in the worked example above as maturity lengthens.

The multi-curve framework, in one picture

The post-crisis solution keeps two curves working side by side, each doing one job only:

In the old single-curve world these were the same curve, so nobody had to keep the two jobs conceptually separate. Post-crisis, a floating payment's size is projected off one curve, and its present value is computed by discounting on a different curve entirely — two curves, doing two genuinely different things, bootstrapped independently from different market instruments (OIS swaps for the discount curve; FRAs and swaps on the floating index for the projection curve).

The 2008 spread widening wasn't LIBOR's last scandal. In 2012, investigators revealed that panel banks had been quietly manipulating their submitted borrowing-rate estimates for years — sometimes to flatter their own trading positions, sometimes to look healthier than they were during the crisis — because LIBOR was, at its core, just banks self-reporting a number nobody could easily verify. The ensuing scandal, billions of dollars in regulatory fines, and the shrinking pool of actual unsecured interbank lending LIBOR was supposed to measure (most bank funding today isn't unsecured interbank lending at all) together convinced regulators that LIBOR needed to be retired entirely. By mid-2023, LIBOR stopped being published for almost all currencies and tenors, replaced in dollar markets by SOFR — the Secured Overnight Financing Rate, built from actual overnight Treasury-repo transactions rather than a survey of opinions. It's a far harder rate to manipulate, precisely because it's anchored to a huge, observable, transaction-based market instead of a phone poll.

It's an easy but wrong inference: "LIBOR is gone, SOFR does everything now, so we're back to one curve." In fact the multi-curve framework survived the LIBOR transition largely intact, just with different names on the two curves. Overnight SOFR, compounded daily in arrears, remains the natural discounting rate (it's what collateral now typically earns). But many swaps still reference a forward-looking Term SOFR rate for setting a period's floating payment in advance — and Term SOFR is bootstrapped from a different set of market instruments than the compounded-overnight-SOFR discounting curve, so the two curves remain genuinely distinct animals, projecting and discounting separately, just as before.

The second common mistake is treating OIS discounting as a minor technical correction that only matters for exotic trades. It doesn't just apply to unusual structures — it applies to essentially every collateralized swap in the market, which by notional is nearly all of them. Getting the discount curve wrong on a large book doesn't just mis-price one trade; it systematically mis-states hedge ratios and P&L across the entire portfolio, which is exactly the kind of quietly compounding error that a risk manager cannot afford to wave away as a rounding issue.