1. Why yield curves are needed

The yield curve is the single piece of market information a corporate treasury team should consult in order to understand the cost of funding across different time horizons. A treasurer deciding whether to refinance a bullet loan in two years or in seven, or whether to hedge a floating exposure for three years or for ten, is implicitly comparing different points on the curve.

The curve plays two roles at once. It is a benchmark for pricing: every loan quote, bond issuance, or swap a bank offers is anchored to it, and a credit margin is added on top. It is also a barometer for economic expectations: the shape of the curve summarises, in a single picture, what the market collectively thinks about future central bank policy, inflation, and growth.

Two practical consequences follow.

First, understanding funding cost is about the entire curve and its shape, not a single rate. A flat curve and a steeply upward sloping curve at the same 5Y level imply very different decisions on whether to fix today, fix later, or stay floating. A treasurer who looks only at one number misses the trade-offs that the rest of the curve makes visible.

Second, the curve is the natural reference point for challenging a price. When a bank quotes a 7-year swap at 3.10% and the published 7-year swap rate is 2.79%, the difference is the bank’s margin or credit spread, not the cost of money. Decomposing a quote into its market level (read from the curve) and its margin or spread (negotiated with the counterparty) is the first step in any price discussion.

This chapter sets the foundation. It introduces the practical language used to talk about curves, the three constructs that practitioners switch between (quote curves, zero-coupon curves, and forward curves), and the ways in which curves move and what those moves typically mean.

2. What a yield curve is

A yield curve is a collection of interest rates for different maturities within a specific market, observed at a single point in time. It is a snapshot of how the price of time varies at that instant, in a single currency, for a single type of borrower.

Three pieces of information are needed to define any curve:

• the currency (EUR, USD, GBP, etc.),
• the issuer or market segment (a sovereign, a swap market, a corporate sector),
• the maturities at which the rates are observed (1 month, 1 year, 10 years, 30 years).

The same currency can have many different curves at the same time, and the differences between them carry meaning.

2.1 Different curves for the same currency

In any major currency, two families of curves dominate.

Government bond curves plot the yields of sovereign debt at different maturities. In EUR, the German Bund curve is the reference (Germany being treated as the euro area’s safest sovereign issuer). In USD it is the US Treasury curve. In GBP, the UK Gilt curve.

Interbank or swap curves plot the fixed rates on standard interest rate swaps at different maturities. They reflect the cost of exchanging fixed for floating cash flows in the interbank market and are the natural reference for pricing OTC derivatives. As a consequence, EUR does not have a single swap curve but multiple market quotes curves, one per floating reference, e.g. an OIS curve built from overnight index swaps referencing €STR, a 3M EURIBOR-linked curve built from swaps paying fixed against 3-month EURIBOR, and a 6M EURIBOR-linked curve built from swaps paying fixed against 6-month EURIBOR. USD and GBP work similarly, with SOFR and SONIA replacing EURIBOR after the LIBOR transition described in Interest rate benchmarks.

The two families differ for two reasons. Government curves are exposed to sovereign credit risk and to supply and demand for sovereign paper. Swap curves reflect the rate at which banks (and now collateralised counterparties) exchange cash flows, with little outright credit risk because swaps do not exchange principal. In a normal market environment, the difference between a swap rate and the equivalent government yield, called the swap spread, is small and reasonably stable. When it widens or inverts, it signals stress in either market.

For most corporate treasury work, the swap curve is the relevant reference. It is the curve against which loans and hedges are priced, and the one shown on bank dealing screens.

A third family is built from corporate bond yields. These curves can be aggregated by credit rating (an AAA curve, a BBB curve, a high yield curve) or by industry (utilities, financials, energy). They sit above the government and swap curves by an issuer-specific credit spread and serve as benchmarks for pricing corporate loans. For an international corporate, an important application is the pricing of intercompany loans under the arm’s length principle. A parent company lending to a subsidiary must set the rate as if the subsidiary were borrowing from an unrelated third party on a standalone basis. Corporate yield curves segmented by credit rating are the typical reference for that calculation. The parent estimates the subsidiary’s credit rating, reads the relevant point on the corresponding corporate curve for the loan’s tenor, and uses that as the benchmark. Other approaches exist, such as comparable uncontrolled price methods based on observed external loans to similar borrowers, but rating-based corporate curves remain the most common practical tool.

2.2 The market quotes curve

What a treasurer actually sees on a Bloomberg or Refinitiv screen is the market quotes curve: a list of par rates for the most liquid instruments at standard maturities. For the EUR swap market, that means OIS rates and EURIBOR-linked swap rates at tenors of 1Y, 2Y, 3Y, … 10Y, 15Y, 20Y, 30Y. Each rate is the fixed leg coupon at which a brand new swap of that maturity would have zero value at inception.

At the very short end (under one year), the most liquid quotes are typically not swaps but Forward Rate Agreements (FRAs) and listed short-term interest rate futures. They serve the same role as par swap rates further out, providing the market quotes that anchor the front of the curve.

This quotes curve is what the market trades. It is the input for every other curve construct (zero-coupon, forward) introduced later in this chapter, but it is not in itself the curve used to value cash flows. That distinction matters.

2.3 Example: the EUR swap curve against 3M EURIBOR

The chart below shows the EUR swap curve quoted against 3-month EURIBOR as of 20 April 2026, taken from the Treasury Toolbox market data set. Each point is the fixed rate on a standard swap of the corresponding maturity. More free market data is available at treasurytoolbox.com/market-data.

A few features stand out. The curve is upward sloping over most of its length. The 1Y swap rate is near 2.47% and then rises to roughly 3.24% at 20Y. Beyond 20Y, the curve flattens and slightly inverts: the 30Y rate (3.20%) is below the 20Y rate (3.24%). This long-end behaviour is not unusual in EUR markets and we return to it in section 7.

When a bank quotes a corporate client a 7-year EUR loan at “3M EURIBOR + 1.50%” or a 7-year fixed loan at “swap + 1.50%”, the implicit reference is the 7Y point on this curve, around 2.79%. The fixed equivalent is approximately 2.79% + 1.50% = 4.29%. Without the curve, the borrower has no way to assess whether the total borrowing rate is fair.

3. Three zones of the curve

Practitioners rarely talk about the curve as a single object. They split it into zones, each driven by different forces and observed through different instruments. The exact boundaries are subjective and vary across desks and use cases. The three-zone split adopted in this chapter (front end, belly, long end) is one common convention. It is convenient for treasury work but should not be read as a hard taxonomy.

3.1 The front end (0 to 2 years)

The front end is dominated by central bank policy and liquidity conditions. Rates here track the current and near-future path of the deposit facility rate (or fed funds rate, or Bank Rate). Movements reflect changes in the expected rate path: a hawkish surprise from the central bank pushes the front end higher, a dovish one pulls it down.

The standard instruments are commercial paper, money market deposits, Forward Rate Agreements (FRAs), short-dated futures, and short interest rate swaps (1Y and 2Y). The chapter The macro drivers of interest & FX rates covers the policy forces that shape this zone in detail.

3.2 The belly (2 to 10 years)

This is the corporate zone, sometimes called the belly of the curve. It is where most corporate bond issuance and most corporate hedging activity sits. Rates here reflect the medium-term outlook for inflation, the economic cycle, and the path of policy rates over several years. They typically incorporate a term premium: extra compensation that lenders demand for committing to a longer horizon than the front end.

The standard instruments are interest rate swaps and corporate bonds with 3 to 10 year maturities. When a treasurer sets a hedging strategy for a typical loan, this is the zone they are operating in.

3.3 The long end (beyond 10 years)

The long end reflects expectations of long-term real growth, structural inflation, and, crucially, structural demand from pension funds and insurers. These investors have liabilities stretching out 20, 30, or even 40 years, and they need long-dated assets to match them. Their demand for 20Y and 30Y bonds and receiver swaps influences long-end rates independently of macro forecasts.

The standard instruments are long-dated government bonds and long-dated swaps. The 20Y to 30Y inversion visible in the chart in section 2.3 is partly a reflection of pension and insurance flows: heavy receiving (paying floating, receiving fixed) at the very long end can pull those rates below the 20Y level.

4. Curve shapes

The most basic property of a curve is its shape. Three archetypes recur.

4.1 Upward sloping (normal)

In an upward sloping curve, longer maturities pay higher rates than shorter ones. This is historically the most common shape and is consistent with two forces working together: the market expects short rates to rise (or at least not fall) over time, and lenders demand a term premium for committing capital over longer horizons. The April 2026 EUR curve in section 2.3 is upward sloping over most of its length.

4.2 Flat

A flat curve has roughly the same rate at all maturities. This is a transitional regime, typically observed when the market is uncertain about the next move in policy rates: enough is priced in for the medium term to push short rates near long rates, but no clear directional view dominates. Flat curves often appear near the end of a hiking cycle, when the central bank is judged to be done but cuts are not yet expected.

4.3 Inverted

In an inverted curve, short rates exceed long rates. This typically signals that the market expects the central bank to cut rates in the future, often because a recession is anticipated. Long-dated lenders effectively accept a lower rate today because they expect short rates to fall sharply.

Curve inversion has historically been a reliable, if imperfect, recession signal in the United States. In the eurozone, deep inversions accompanied the rapid hiking cycle of 2022 to 2023 and the subsequent expectation of cuts. The interpretation always depends on the regime and the curve observed: an inverted government curve and an inverted swap curve do not necessarily carry identical meanings.

5. Curve moves and their meanings

The curve shifts every day. To talk about those shifts, the market uses a stable vocabulary borrowed from the bond market.

5.1 Level moves: bull and bear

A bull move is a fall in rates. Bond prices rise, hence the “bull” terminology from the bond market perspective. A bear move is a rise in rates: bond prices fall.

Pure level moves (where the entire curve shifts up or down in parallel) are rare in practice. Rates at different maturities are driven by different forces, so the curve usually changes shape as it moves.

5.2 Slope moves: steepening and flattening

The slope of the curve is typically measured as the spread between two reference maturities. The most watched spreads are the 2s10s (10Y rate minus 2Y rate) and the 5s30s (30Y rate minus 5Y rate).

A steepening is a widening of those spreads: long rates rise more than short rates, or short rates fall more than long rates. A flattening is the opposite: spreads tighten. An inversion is an extreme flattening in which the spread becomes negative.

5.3 Combined narratives

Slope and level moves are usually combined. The market identifies four standard combinations, each with its own typical economic narrative.

Bull steepening. The front end falls more than the long end. Both rates drop, but short rates drop faster, so the curve steepens. This usually reflects the market pricing in imminent policy easing: the central bank is expected to cut soon, pulling the short end down sharply, while long rates fall less because long-term inflation and growth expectations have not changed as much.

Bull flattening. The long end falls more than the front end. This is typically a risk-off signal. Investors flock to long-dated safe assets (a flight to quality), pushing long yields down. The front end is anchored by the current policy rate and moves less.

Bear steepening. The long end rises more than the front end. This is the classic signal of rising inflation expectations or a higher term premium. The market is not necessarily pricing in higher policy rates today, but it demands more compensation for committing to long horizons.

Bear flattening. The front end rises more than the long end. This is the signature of an aggressive tightening cycle: the central bank is hiking, the market prices in more hikes, and short rates rise sharply. Long rates rise less because the market expects the hikes to slow growth and eventually require cuts.

5.4 Curvature

Real curve moves are rarely as clean as a uniform steepening or flattening. A common pattern, especially around turning points in the cycle, is a convexity move: different segments of the curve move in opposite directions. A 2Y to 5Y steepening combined with a 5Y to 10Y flattening, for example, produces a curve with a pronounced hump or kink in the belly.

These kinks matter because they affect different hedges differently. A 5Y swap and a 10Y swap can move in opposite directions on the same day. Treasurers running mixed-maturity hedge programmes need to look at the whole curve, not just a single benchmark.

6. Macro drivers vs flow drivers

The narratives in section 5 attribute curve moves to macroeconomic forces: central bank policy, inflation expectations, growth expectations, term premium. The chapter The macro drivers of interest & FX rates covers those forces in detail. In practice, not every curve move is a macro signal. Flow and supply-demand effects can be just as important, especially at specific points on the curve.

Two examples are familiar to practitioners.

Corporate payers in the belly. All the corporates typically hedge their floating loan portfolio by paying fixed in 5Y to 10Y swaps. The aggregate paying flow from the corporate sector lifts swap rates in the belly relative to the rest of the curve.

Pension funds and insurers at the long end. These investors are structural receivers of fixed at the long end (paying floating, receiving fixed), driven by the need to match long-dated liabilities. Their flows pull long swap rates lower relative to where macro forces alone would put them.

A specific case is currently reshaping EUR long-end swap rates: the Dutch pension reform. The Dutch pension system, the largest in the eurozone, is transitioning from defined benefit schemes (with very long-dated liabilities, hedged via large receiver positions in 30Y and longer swaps) to defined contribution schemes, in which the duration of hedging needs is significantly shorter. As funds reduce their ultra-long receiving positions over the multi-year transition, demand for long-end fixed receiving falls, putting upward pressure on long-end swap rates relative to where they would otherwise sit.

7. The zero-coupon curve

The market quotes curve in section 2 is the curve that is traded. It is not, however, the curve used to value cash flows. For valuation, practitioners need a different construct: the zero-coupon (ZC) curve, also called the discount curve.

7.1 Why a single rate is not enough

Consider valuing a 10Y interest rate swap. The swap has roughly 40 quarterly cash flows on the floating leg and 10 annual cash flows on the fixed leg, each paid at a different date. As the chapter Time value of money & discount factors establishes, the value of any financial instrument is the sum of its future cash flows, each discounted to today:

You cannot use a single “10Y swap rate” of 2.96% to discount every one of those cash flows. The cash flow arriving in 6 months should be discounted at a 6-month rate. The cash flow arriving in 9 years should be discounted at a 9-year rate. Each cash flow needs its own discount factor.

The zero-coupon curve provides exactly that: a discount factor $\text{DF}(t)$ for every relevant date $t$. Equivalently, since

(under the continuous compounding convention used in derivatives pricing) it provides a zero rate $r(t)$ for every maturity. The zero rate $r(t)$ is the rate at which a single cash flow at date $t$ would be discounted on its own. It corresponds to the yield on a hypothetical zero-coupon bond paying 1 at $t$.

7.2 The ZC curve is not directly observed

Zero-coupon bonds for arbitrary maturities are not actively traded in most markets. The ZC curve must therefore be constructed from the prices of liquid instruments, typically the par swap rates from the quotes curve, plus short-dated deposits and futures at the front end. The procedure is called bootstrapping: maturities are processed sequentially, each new ZC point chosen so that the corresponding traded instrument prices to par.

The full bootstrapping procedure will be the subject of a future chapter.

For euro valuation, the discount curve is built from market rates linked to the €STR, which is the OIS curve. The EURIBOR-linked curves of section 2.3 are used to project floating payments, as section 8.3 explains. The chapter Net present value & basis point value explains which discount curve to use (section 2.6).

8. The forward rate curve

The third construct sits alongside the par curve and the zero curve and is just as important for treasurers.

8.1 Spot vs forward

A spot rate answers the question: how much does it cost to borrow from now to a date $T$? The 5Y spot rate is the rate to borrow today for the next five years.

A forward rate answers a different question: how much would it cost to borrow for a period $\tau$, starting at some date $T_1$ in the future? The 1y1y forward rate is the rate to borrow for one year, starting one year from now. The 5y10y forward rate is the rate to borrow for ten years, starting five years from now.

The forward rate curve is a collection of these forwards across different start dates, for a fixed reference rate (e.g. 3M EURIBOR). It is the market-implied path of the reference rate in the future.

This matters enormously in practice. The floating leg of an interest rate swap (or a floating rate loan) pays interest based on future fixings of the reference rate, fixings that have not yet happened. To value such a leg today, those unknown future fixings must be replaced by the market’s best estimate. The forward rate curve provides exactly that estimate, and the chapter Pricing interest rate swaps shows how it is used in valuation.

8.2 Deriving a forward from no-arbitrage

Forward rates are not separate market quotes. They are implied from the zero-coupon curve by no-arbitrage. The reasoning is direct: an investor with two years of cash to lend has two strategies. Strategy A is to lend for two years at the 2Y zero rate $r_2$. Strategy B is to lend for one year at the 1Y zero rate $r_1$, then re-lend the proceeds for the second year at a rate $f(1,2)$ agreed today for that future period. Using the annual compound interest convention, if the two strategies are to deliver the same total return, the forward rate $f(1,2)$ must satisfy:

Equivalently, in terms of discount factors:

The forward “fills the gap” so that an investor is indifferent between the two strategies. Any other forward rate would create an arbitrage opportunity.

The same logic generalises to any pair of dates. The 5y5y forward rate (5-year rate starting in 5 years), the 10y10y forward, and so on, are all derived from the zero curve by exactly this no-arbitrage relationship.

8.3 What forward curves are useful for

For a corporate treasurer, the forward curve is the practical answer to several common questions.

• Projecting floating cash flows. A swap or floating rate loan paying 3M EURIBOR + 1.50% over five years has unknown future coupons. The 3M forward curve provides the market’s best implied path for those EURIBOR fixings, which is what banks and pricing systems use for projection.
• Reading what the market prices in. The 1y1y forward says, in one number, where the market expects the 1Y rate to be in a year. A treasurer comparing today’s 1Y to the 1y1y forward sees directly whether the market is pricing in hikes or cuts.
• Explaining hedge value changes. A floating leg can move in value before today’s fixing changes, simply because forward rates further out have shifted. Without the forward curve, the daily P&L on a swap is hard to interpret.

8.4 An important caution: implied is not forecast

Forward rates are sometimes called the “expected future rate”. This is loose language and can mislead. The forward rate is the arbitrage-free, no-free-lunch rate consistent with today’s zero curve. It is not a forecast.

The gap between the two has several sources. Forwards include a term premium, the extra compensation lenders demand for committing over longer horizons. They reflect liquidity effects that distort certain segments of the curve. They embed supply and demand imbalances (such as the pension flows in section 6) that have no direct macro interpretation. Empirically, forward rates are often biased estimators of where rates actually end up.

That said, forwards remain the standard reference for valuation. The right way to think about them is operational: they are what the market collectively agrees to use to value cash flows today, and any pricing or hedging done with them is consistent with current quotes. Using them as forecasts is a separate exercise, and a riskier one.

9. Key takeaways

• The yield curve is the treasurer’s most important reference: a benchmark for pricing, a barometer for economic expectations, and the foundation of every valuation in this Knowledge Hub.
• Funding decisions depend on the shape of the curve, not a single rate. The curve is also the natural reference point for decomposing a quote into a market level plus a margin or spread.
• A yield curve is a collection of interest rates for different maturities, in a single currency, for a single market segment. The same currency has multiple curves: government bond curves, OIS curves, EURIBOR-linked or SOFR-linked swap curves.
• The market quotes curve is what a screen displays: par rates for liquid instruments at standard maturities. It is what the market trades, but not what is used directly to value cash flows.
• The curve has three zones. The front end (0 to 2Y) is driven by central bank policy. The belly (2 to 10Y) is the corporate zone, driven by inflation and cycle expectations. The long end (beyond 10Y) is shaped by long-term growth expectations and structural demand from pension funds and insurers.
• Standard shapes are upward sloping (most common, term premium plus growth expectations), flat (transitional regime), and inverted (expected easing or recession risk).
• Curve moves combine level (bull or bear) and slope (steepening or flattening) into four standard narratives: bull steepening (priced-in easing), bull flattening (risk-off), bear steepening (rising inflation or term premium), and bear flattening (aggressive tightening).
• Real moves often involve curvature changes, with different segments of the curve moving in opposite directions.
• Not every curve move is a macro signal. Flows matter: corporate paying in the belly lifts mid rates, pension and insurance receiving at the long end pulls long rates lower. The Dutch pension reform is a current example of a structural flow shift putting upward pressure on EUR long-end swap rates.
• The zero-coupon (ZC) curve, also called the discount curve, is the curve actually used for valuation. The discount factor for date $t$ is $\text{DF}(t) = e^{-r(t) \cdot t}$. Each cash flow uses its own discount factor. There is no single “10Y rate” to value a 10Y instrument.
• The ZC curve is not directly observed. It is derived from the quotes curve via bootstrapping.
• The forward rate curve is the market-implied path of a reference rate in the future. Forwards are derived from the zero curve by no-arbitrage: $(1 + r_2)^2 = (1 + r_1) \times (1 + f(1,2))$.
• For treasurers, the forward curve is the practical tool for projecting floating cash flows, reading what the market prices in, and explaining day-to-day hedge value changes.
• Implied is not forecast. Forwards include term premia, liquidity effects, and supply-demand imbalances. They are the standard reference for valuation, but should not be confused with predictions of future rates.