Yield Curve Explorer: Term Structure of Interest Rates

Curve Shape (Nelson-Siegel)

Level β₀ — long-run rate 4.00%

Slope β₁ — short minus long 2.00%

Curvature β₂ — mid-curve hump -1.00%

Decay λ — hump position 1.50

Presets

Live Readouts

Steep normal curve

2Y – 10Y spread

— bps

1Y1Y forward rate

—%

3M yield

—%

30Y yield

—%

How it works

The yield curve plots the interest rate (yield) that bonds of the same credit quality pay across different maturities — 3-month T-bills up to 30-year bonds. Its shape is modelled here with the Nelson-Siegel parametric curve, the same functional form central banks use to fit real term structures:

y(τ) = β0 + β1 · (1 − e^(−τ/λ))/(τ/λ)
            + β2 · [(1 − e^(−τ/λ))/(τ/λ) − e^(−τ/λ)]

β0 (level) — the rate all maturities converge to as τ → ∞: the long-run anchor.
β1 (slope) — the short-rate minus the long-rate. Positive β1 makes short yields sit below long yields (a normal curve); negative β1 pushes short rates above long rates (inverted).
β2 (curvature) — controls a hump or dip around medium maturities.
λ (decay) — sets which maturity the hump sits at; smaller λ moves it toward shorter maturities.

The 2s10s spread (10-year yield minus 2-year yield) is the classic recession signal: it has gone negative — an inverted curve — before every US recession since 1955, because it means the market expects the central bank to cut short-term rates in the future.

The 1Y1Y forward rate is the rate the market implies for a one-year loan starting one year from now, backed out from the 1-year and 2-year spot yields via no-arbitrage:

(1 + y2)² = (1 + y1) · (1 + f1,2)
f1,2 = (1+y2)² / (1+y1) − 1

The scene renders today's curve as bars across maturity, with a fading trail of recent curve shapes receding into the distance — a live "term-structure surface" showing how the curve moves through time, exactly as traders watch it on a Bloomberg terminal.

Current yield curve Recent history (fading) Inverted segment

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