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Bond Price & Duration Lab (2D)

Q: Why is convexity needed on top of duration?

The true price-yield relationship is curved (convex), not a straight line, so the duration-only estimate systematically understates the actual price at both higher and lower yields. Adding a convexity correction term captures that curvature and closes most of the gap.

2D bond-pricing lab: adjust face value, coupon rate, maturity and market yield, and watch the true present-value price curve bow against the duration and duration-plus-convexity estimates.

Financial Models & Markets2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion drives the same present-value bond math as the 3D version through a plain price-yield chart: sliders control face value, coupon rate, maturity and the market yield, and the chart plots the true discounted-cash-flow price curve alongside a duration-only straight-line estimate and a duration-plus-convexity estimate, so you can see exactly how much the linear approximation misses and how the convexity term closes that gap as the yield moves away from the bond's own coupon rate.

⚙ Under the hood

2D bond-pricing lab: adjust face value, coupon rate, maturity and market yield, and watch the true present-value price curve bow against the duration and duration-plus-convexity estimates.

bondsdurationconvexityinterest ratesfixed incomepresent value

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

❓ FAQ

Why do bond prices fall when interest rates rise?
A bond's price is the present value of its future coupon and face-value payments, discounted at the current market yield. When the market yield rises, each future cash flow is discounted more heavily, so the sum of their present values — the price — falls.

What is duration, and what does it estimate?
Modified duration approximates the percentage change in a bond's price for a 1 percentage-point change in yield. It comes from Macaulay duration (the present-value-weighted average time to receive the bond's cash flows) divided by (1 + yield).

Why is convexity needed on top of duration?
The true price-yield relationship is curved, not straight, so the duration-only estimate systematically understates the actual price at both higher and lower yields. The convexity term captures that curvature.