LIBOR Curve

A LIBOR curve organized historical LIBOR tenor fixings or projected future LIBOR cash flows; it is now a legacy curve requiring date, currency, and methodology checks.

A LIBOR curve is a historical term for either a set of published LIBOR fixings across maturities or a model-built curve used to project future LIBOR-linked cash flows. All LIBOR settings have ceased, so a LIBOR curve is now relevant to legacy contracts, historical valuation, transition analysis, and old market data rather than new benchmark publication.

The label is ambiguous. An analyst must determine whether a source means a same-day chart of historical tenor fixings, such as one-, three-, and six-month LIBOR, or a bootstrapped forward curve built from market instruments. Those are related but not interchangeable datasets.

Key Takeaways

  • LIBOR was a family of currency-and-tenor settings, not one interest rate.
  • A tenor-fixing curve joined published LIBOR settings observed on one date.
  • A LIBOR projection curve estimated future LIBOR fixings from deposits, futures, forward-rate agreements, and swaps.
  • The published fixings were trimmed averages of eligible panel-bank submissions, not simple averages of every submission.
  • A forward point derived from a curve was not a forecast or a guaranteed future fixing.
  • Discounting and projecting often used different curves after the financial crisis.
  • All LIBOR settings have ceased; current work should not treat the curve as a live administered benchmark.
  • Historical valuation requires the correct currency, observation date, tenor, conventions, and contemporaneous market inputs.

Two Meanings of LIBOR Curve

MeaningMain inputsWhat the curve showedTypical use
Published-tenor curveLIBOR fixings for several maturities on one dateHistorical term structure of panel-based bank funding ratesMarket commentary and historical comparison
Projection or forward curveMarket prices from LIBOR-linked instrumentsImplied future LIBOR reset ratesPricing floating cash flows, hedging, and scenario analysis

A chart of the published one-month, three-month, six-month, and twelve-month settings was not enough to value a long-dated swap. That valuation normally required a curve-construction process extending beyond the published LIBOR tenors.

Historical LIBOR Tenor Fixings

LIBOR settings were identified by both currency and tenor. A three-month U.S. dollar setting and a three-month sterling setting represented different markets and could not be combined into one curve.

The administrator calculated each eligible setting from panel-bank submissions after removing specified high and low observations under the applicable methodology. The result was therefore a trimmed mean, not:

$$ \frac{\text{sum of all submissions}}{\text{number of submissions}} $$

That simple-average expression omits the trimming rules and should not be used to reconstruct a historical fixing.

How a LIBOR Projection Curve Was Built

Before cessation, a curve builder could combine instruments covering different maturity ranges, such as:

  • short-dated deposits or published fixings
  • interest-rate futures or forward-rate agreements
  • fixed-for-floating interest-rate swaps
  • basis swaps connecting different tenors

The model solved for discount factors or forward rates that reproduced the observed instrument prices under stated conventions. The output depended on quote time, interpolation, day count, business-day adjustments, collateral assumptions, and instrument liquidity.

There was no single universal LIBOR curve. Two vendors could produce different curves from the same broad market if their inputs, cut-off times, interpolation methods, or treatment of outliers differed.

Worked Example: Implied Three-Month Forward LIBOR

Assume a historical simple-money-market curve showed:

  • three-month rate: 5.00%
  • six-month rate: 5.20%
  • each three-month period has a year fraction of 0.25

The simple three-month rate beginning in three months, f_{3,6}, can be inferred by matching the six-month accumulation with two consecutive three-month periods:

$$ \left(1+0.0520\times0.50\right) = \left(1+0.0500\times0.25\right) \left(1+f_{3,6}\times0.25\right) $$

Solving gives:

$$ f_{3,6} = \frac{ \frac{1+0.0520\times0.50}{1+0.0500\times0.25}-1 }{0.25} \approx 5.33\% $$

The 5.33% is a curve-implied forward rate under the example’s conventions. It is not a prediction that the future three-month LIBOR fixing would equal 5.33%.

Projection Curve vs. Discount Curve

Older single-curve models often used one LIBOR curve both to project floating payments and to discount them. Following changes in funding, collateral, and derivatives markets, multi-curve valuation became common:

  • a tenor-specific curve projected the floating reference rate
  • an overnight-index curve discounted collateralized cash flows
  • basis spreads reconciled economically different tenors or curves

Using one curve for both roles after the valuation framework had changed could materially misstate value and risk. The applicable collateral agreement and market convention were part of the model, not administrative details.

What LIBOR Cessation Changed

All LIBOR settings have permanently ceased. A historical LIBOR curve can still support:

  • reconstruction of legacy cash flows
  • valuation-date back-testing
  • hedge and basis analysis
  • transition-spread review
  • accounting or litigation evidence

It should not be extended into current periods by merely carrying forward the last fixing. A surviving legacy contract may use a contractual fallback, a statutory replacement, a synthetic setting for a permitted historical period, or another defined rate. The governing document determines the result.

Post-LIBOR curves built from SOFR, SONIA, or another overnight benchmark are not renamed LIBOR curves. Their underlying markets, compounding conventions, credit content, and payment timing differ.

How to Review a Legacy LIBOR Curve

  1. Identify the currency and every tenor represented.
  2. Record the observation date, publication time, and data source.
  3. Separate published fixings from model-implied forwards.
  4. List the instruments used to extend or bootstrap the curve.
  5. Confirm day-count, compounding, calendars, and interpolation.
  6. Determine which curve projected cash flows and which discounted them.
  7. Check collateral, clearing, and basis assumptions.
  8. Preserve the version of the curve used in the original valuation.
  9. Apply the contract’s fallback rather than assuming a universal replacement.
  10. Reconcile any hedge using its own benchmark and transition terms.

Common Mistakes and Limitations

  • Describing LIBOR or a LIBOR curve as currently published.
  • Treating LIBOR as one rate without currency and tenor.
  • Using a simple average of all panel submissions.
  • Calling a chart of tenor fixings a complete valuation curve.
  • Treating an implied forward rate as a certain forecast.
  • Mixing simple, annual, and continuous compounding.
  • Projecting and discounting with one curve without checking the valuation framework.
  • Replacing LIBOR with SOFR one-for-one without fallback, spread, and convention analysis.
  • Ignoring stale, indicative, or illiquid curve inputs.

Authoritative Sources

  • LIBOR: The discontinued benchmark family underlying historical LIBOR curves.
  • Forward Rate: Future-period rate implied by a current curve.
  • SOFR: Secured overnight benchmark used in many U.S. dollar post-LIBOR contracts.
  • Alternative Reference Rates: Benchmarks and conventions used in IBOR transition.
  • Interest Rate Swap: Instrument historically used to extend LIBOR projection curves.

FAQs

Is a LIBOR curve still published?

No live LIBOR settings remain. Vendors and institutions may retain historical LIBOR curves or construct legacy valuation curves, but these are not new LIBOR benchmark publications.

Was the LIBOR curve the same as the yield curve?

No. It was one market-specific curve based on unsecured bank-funding benchmarks and related instruments. Government, overnight-index, issuer, and discount curves can have different levels and uses.

Can SOFR simply replace the LIBOR curve?

No. SOFR is an overnight secured benchmark with different economics. Contracts and models need the specified fallback, spread treatment, compounding method, and discounting framework.

This article provides general financial education, not personalized investment, derivatives, accounting, or legal advice. Historical valuation should use contemporaneous data, documented model conventions, and the governing contract.