Funding and Projection Curves

Summary
Detail
See also

Summary

Many interest rate curves share a fundamental relationship: they form a family containing one main curve for discounting — the Funding Curve — and a set of Projection Curves hanging off it, one per floating index tenor (3M, 6M, 12M, …). Every Projection Curve depends on the Funding Curve for discounting; none discounts using its own rates. Curve identity (Funding, EURIBOR-3M, EURIBOR-6M, …) is a small, discrete, categorical label — not a second continuous axis alongside tenor — so a family is best understood as an anchor curve plus an enumerable set of dependent curves, not a two-dimensional field.

Detail

Structure

                       ┌───────────────────────┐
                       │    FUNDING CURVE      │   ← the discounting anchor
                       │  (e.g. OIS / collat.) │
                       └──────────┬────────────┘
                                  │ all cash flows discounted here,
                                  │ regardless of which curve
                                  │ projects them
      ┌───────────────┬───────────┼────────────────┬────────────────┐
      ▼               ▼           ▼                ▼                ▼
┌────────────┐  ┌────────────┐ ┌────────────┐ ┌────────────┐  ┌───────────┐
│ Projection │  │ Projection │ │ Projection │ │ Projection │  │   ...     │
│  1M        │  │  3M        │ │  6M        │ │  12M       │  │           │
└────────────┘  └────────────┘ └────────────┘ └────────────┘  └───────────┘
 (index tenor)   (index tenor) (index tenor)  (index tenor)

Each curve in the family is itself bootstrapped from its own set of pillar instruments, curve template, and parameters — see Interest Rate Curves for the single-curve bootstrapping mechanics (day-count conventions, pillar instruments, interpolation). What makes the set a family rather than a pile of unrelated curves is the discounting dependency: every Projection Curve's cash flows are always discounted via the Funding Curve, which also constrains when each curve can be built — see Multi-Curve Construction.

Curve identity is discrete, not continuous

An anchor curve plus a discrete, enumerable set of dependent curves is best called a curve family: the only continuous axis is tenor (time along one curve). Curve identity is a small categorical label — there is no meaningful "curve between EURIBOR-3M and EURIBOR-6M", only a discrete choice of which independently-bootstrapped curve applies to a given cash flow. That label also carries a benchmark type — see Interest Rate Benchmark Types: IBOR vs. RFR.

Not the CRM's driver/derived pattern

The FX cross-rates matrix uses a superficially similar-sounding split — driver and derived rates — and it is tempting to map Funding→driver, Projection→derived. Resist that: the two relationships work by a different mechanism.

CRM derived rate: has no market quotes of its own. Its value is computed from driver rates by triangulation (e.g. EUR/GBP derived = EUR/USD driver ÷ GBP/USD driver). Which rates are drivers vs. derived is also a choice — a spanning-tree selection over an otherwise symmetric graph, not an inherent asymmetry between the rates themselves.
Projection Curve: has its own market quotes — it is bootstrapped from its own pillar instruments (e.g. 3M-EURIBOR swaps), exactly as the Funding Curve is bootstrapped from OIS instruments. Its rates are not a computed function of the Funding Curve's rates. The dependency is a construction- order one only: the Funding Curve must exist first because a Projection Curve's own pillar instruments need it to discount their cash flows during bootstrap (see Multi-Curve Construction). Once built, a Projection Curve's rates come from its own market. And unlike CRM drivers/derived, which curve is the Funding Curve is not a free choice — it is always the collateralised/OIS curve, never a Projection Curve wearing that hat.

So the terms deliberately differ: anchor and dependent here, not driver and derived — the mechanism is "must build first, discount with", not "compute this one from that one".

Cost/simplification trade-off

Maintaining a full Projection Curve for every floating index tenor (3M-in-3M, 3M-in-6M, 3M-in-9M, … out to the swap's maturity) is expensive. The common simplification is to maintain a single Projection Curve per currency and approximate projections for other tenors via forward-forward interest rates computed off that one curve — the same forward-forward technique used for volatility interpolation across FX Volatility Surface pillars. In practice, a family is therefore usually smaller than the theoretical full set of per-tenor projection curves, reinforcing that "curve type" is a small, deliberately-curated set rather than a continuum.