Bond Price & Duration from the Yield Curve (2D)

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

Bond

Coupon rate (semiannual) 4.00%

Maturity 10 yr

Stress Test

Parallel yield shift Δy +0.00%

Live Readouts

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Bond price

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2Y–10Y spread

— bps

Effective duration

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Effective convexity

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Price at current Δy — actual vs. duration+convexity estimate

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How it works

The same Nelson-Siegel spot-rate curve as the 3D version of this sim generates the term structure:

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

Instead of drawing the curve as a 3D bar surface, this version prices a real coupon bond off it: every semiannual cash flow is discounted at the spot rate for its own maturity, read straight from the curve (bond-equivalent, per-period compounding — the market-standard convention, which is why a coupon that matches a flat curve prices to exactly 100):

P = Σ CFₜ / (1 + y(t)/2)^(2t)

Duration and convexity are derived the honest way — bump-and-reprice the whole curve by a small parallel shift Δy and measure the response — rather than assumed from a textbook formula, so they correctly reflect discounting off a full curve instead of a single flat yield:

EffDur  = −(P(+h) − P(−h)) / (2h·P0)
EffConv = (P(+h) + P(−h) − 2P0) / (h²·P0)
P(Δy) ≈ P0·(1 − EffDur·Δy + ½·EffConv·Δy²)

β1 (slope) — at τ→0 the curve reads β0+β1 (the short end); at τ→∞ it reads β0 (the long end). So β1 itself is short minus long: negative β1 gives a normal, upward-sloping curve; positive β1 gives an inverted one. (Note: an earlier build of the 3D companion sim had this sign backwards in its preset labels — verified numerically here and corrected.)
Price-yield chart — the true repriced curve is convex, bowing above both its own tangent line (duration alone) and matching the convexity-corrected parabola far more closely at large shifts. That gap between the straight tangent and the true curve is convexity, made visible instead of asserted.
2s10s spread — 10Y yield minus 2Y yield, the same recession signal as the 3D version; it turns the badge red the instant it goes negative.

Spot yield curve Discounted cash flow (PV) Inverted segment