What is bond convexity?

Convexity measures the rate of change of duration as yields change. A bond with higher convexity loses less price when yields rise and gains more when yields fall, making it more valuable in volatile rate environments.

What is modified duration?

Modified duration estimates the percentage price change of a bond for a 1% (100 bps) change in yield. A modified duration of 5 means the bond price moves roughly 5% for each 1% yield shift.

How accurate is the duration-convexity price estimate?

The estimate is a second-order Taylor approximation: ΔP/P ≈ -ModDur × Δy + 0.5 × Convexity × (Δy)². It is very accurate for small yield changes (±200 bps) but may diverge for large shifts.

Why does convexity matter more for long-duration bonds?

Long-maturity bonds have cash flows far in the future, which are discounted at a compounding nonlinear rate. This nonlinearity makes the price-yield curve more curved (higher convexity), giving investors more upside and less downside.

What yield and coupon inputs should I use?

Enter rates as percentages (e.g., 5 for 5%). The yield to maturity (YTM) should reflect the current market rate for that bond. If you only know the bond's price, you would need a separate YTM solver to find the yield first.

Does the calculator handle zero-coupon bonds?

Yes. Set the coupon rate to 0. The Macaulay duration of a zero-coupon bond equals its maturity, and convexity is purely a function of maturity and yield.

Bond Convexity Calculator

Enter bond parameters to instantly calculate modified duration and convexity, then estimate price change for any yield shift.

Bond Parameters

Face Value ($)

Annual Coupon Rate (%)

Yield to Maturity (%)

Years to Maturity

Coupon Frequency

Bond Price

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Present value of cash flows

Macaulay Duration

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Weighted avg time (years)

Modified Duration

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% price change per 1% yield

Convexity

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Second-order rate sensitivity

Price Change Estimator

Yield shift: 0 bps

Duration Effect

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Convexity Effect

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Est. New Price

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Formula: ΔP/P ≈ −ModDur × Δy + 0.5 × Convexity × (Δy)²

Cash Flow Schedule

Period	Time (yr)	Cash Flow	PV

Enter bond parameters and click Calculate.

Summary

Bond convexity measures the curvature of the price-yield relationship, complementing modified duration which only captures linear sensitivity. Together, they let fixed-income investors accurately estimate how much a bond's price will change when interest rates move. This calculator supports both annual and semi-annual coupon bonds and shows a full cash flow breakdown.

How it works

Enter the bond face value, annual coupon rate, annual yield to maturity, and years to maturity.
Select the coupon frequency (annual or semi-annual).
The calculator discounts each cash flow to find the current price.
Macaulay duration is computed as the weighted average time to each cash flow.
Modified duration = Macaulay duration / (1 + yield per period).
Convexity is computed from the second-order weighted sum of discounted cash flows.
Use the yield-change slider to see the estimated new price using the duration-convexity approximation.

Use cases

Assess interest rate risk before buying or selling a bond.
Compare rate sensitivity across bonds with different maturities and coupons.
Estimate portfolio value change after a central bank rate decision.
Understand why high-convexity bonds outperform low-convexity bonds in volatile rate environments.
Teach or learn fixed-income concepts with live, interactive numbers.
Screen bonds for immunization strategies that match asset and liability durations.

Frequently Asked Questions

Last updated: 2026-05-25 · Reviewed by Nham Vu