Bond Convexity Calculator
Estimate how a bond's price changes for a given shift in yield using duration and convexity. Enter the modified duration, convexity, and yield change to see the estimated percentage price change.
Formula
ΔP/P ≈ −Duration×Δy + 0.5×Convexity×(Δy)^2
- Duration gives the first-order (linear) price sensitivity to yield changes; convexity adds the second-order correction.
- Price change ≈ −Duration × Δy + 0.5 × Convexity × (Δy)², with Δy as a decimal (50 bps = 0.005).
- The convexity term is always positive, so it raises estimated prices for both up and down yield moves.
- Including convexity is most important for large yield changes and long-duration bonds.
- This is an approximation; exact repricing requires discounting each cash flow at the new yield.
Duration 6.5, convexity 55, +50 bps
Inputs
- Modified Duration: 6.5
- Convexity: 55
- Yield Change (bps): 50
Δy = 0.005. Price change ≈ −6.5×0.005 + 0.5×55×0.005² ≈ −3.18%, slightly less of a drop than duration alone predicts.
Frequently asked questions
What is bond convexity?
Convexity measures how a bond's duration itself changes as yields move, capturing the curvature of the price–yield relationship.
Why add convexity to duration?
Duration alone assumes a straight line. Convexity corrects for the curve, improving accuracy for larger yield moves.
Is high convexity good?
Generally yes — higher convexity means prices rise more when yields fall and fall less when yields rise, all else equal.
How do I enter the yield change?
Enter it in basis points (1 bp = 0.01%). The calculator converts it to a decimal internally.
Does this give an exact price?
No. It is a second-order estimate. For precise pricing, discount the bond's cash flows at the new yield to maturity.