Bond Convexity Calculator
Created by: James Porter
Last updated:
Estimate bond convexity and compare a duration-only rate-shock estimate with a convexity-adjusted estimate and the exact repriced result.
Bond Convexity Calculator
FinanceAdd convexity to a duration-based rate-shock estimate and compare both shortcuts with exact bond repricing.
What is a Bond Convexity Calculator?
A bond convexity calculator measures the curvature in the bond price-yield relationship and uses that extra information to improve rate-shock estimates.
It sits one step beyond modified duration.
This matters because duration alone assumes a straight-line relationship between yields and prices, but real bond pricing curves.
The bigger the rate move, the more that curvature matters.
A useful convexity calculator should show the convexity measure itself, the duration-only estimate, the duration-plus-convexity estimate, and the exact repriced result.
How the Convexity Calculation Works
The calculator starts with the same discounted cash-flow structure used in bond pricing and duration analysis.
It then estimates how the slope of the price-yield curve changes as yield moves up or down.
That second-order term is combined with modified duration to produce a more accurate price-change estimate for larger interest-rate shocks.
Core convexity relationships
Duration-only price change (%) ≈ -modified duration × change in yield
Duration + convexity estimate adds 0.5 × convexity × (change in yield)^2
Convexity improves approximation when the rate shock is large enough for curvature to matter
Example Scenarios
Example 1: Large rate move
A 1% rate shock often shows a visible gap between duration-only and duration-plus-convexity estimates.
Example 2: Longer bonds
Longer-duration bonds often show larger curvature effects, which makes convexity more valuable.
Example 3: Quality of estimate
Comparing the convexity-adjusted estimate with exact repricing reveals whether the shortcut is still close enough for the decision.
How People Use This Calculator
- Improve rate-risk estimates beyond duration alone.
- Compare bonds with similar duration but different curvature characteristics.
- Stress-test fixed-income positions under larger yield moves.
- Understand why exact repricing can differ from a simple linear estimate.
Tips for Better Convexity Analysis
Use convexity as a refinement, not a replacement for judgment.
Callable bonds and credit-driven repricing can still behave differently from plain-vanilla bond math.
Pair convexity with duration, maturity, and coupon context so the result stays interpretable instead of becoming an isolated number.
Frequently Asked Questions
What is convexity in bonds?
Convexity measures the curvature in the bond price and yield relationship. It helps explain why duration alone becomes less accurate for larger rate changes.
Why is convexity useful?
It improves rate-sensitivity estimates by adding a second-order adjustment on top of modified duration.
Does positive convexity help investors?
Positive convexity is generally favorable because price gains when yields fall can be larger than the losses predicted by a purely linear estimate.
Why compare three estimates?
Seeing duration-only, duration-plus-convexity, and exact repricing together shows how much accuracy the convexity adjustment adds.
Sources and References
- Fixed-income risk references covering convexity and second-order price sensitivity.
- Bond portfolio materials explaining why convexity improves larger-shock estimates.
Planning Note
Bond Convexity Calculator is a planning estimate. Live bond prices can differ because of accrued interest, call features, credit risk, taxes, and market liquidity.