Bond Convexity Calculator — Duration & Convexity for Fixed-Income
Enter the face value, coupon rate, yield to maturity and maturity of a bond to calculate its price, modified duration and convexity — the three key measures of interest-rate risk used in fixed-income portfolio management.
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Coupon payments per year
Curvature of the price–yield relationship (higher = more price upside when yields fall)
How does this calculator work?
Bond convexity = (1/P·m²) × Σ t(t+1)·CFₜ/(1+yₘ)^(t+2) measures the curvature of the price–yield curve. Combined with modified duration (linear sensitivity), it gives a more accurate price-change estimate: ΔP/P ≈ −ModD·Δy + ½·Convexity·Δy². Higher convexity means the bond gains more when yields fall and loses less when they rise.
Formula
How this is calculated
A coupon bond's price P is the present value of all future cash flows — periodic coupon payments (Face × c/m) plus the face value at maturity — discounted at the yield per period yₘ = YTM/m: P = Σ CFₜ / (1+yₘ)ᵗ. Modified duration measures the first-order (linear) price sensitivity to yield: for a 1 percentage-point yield increase, the bond price changes by approximately −ModDuration × P × 0.01. Convexity measures the second-order (curvature) effect: the true price–yield relationship is curved (convex), not linear, and convexity captures how much the duration itself changes as yields move.
Convexity is computed as the second derivative of price with respect to yield, scaled by price: Convexity = (1/P·m²) × Σ t(t+1)·CFₜ/(1+yₘ)^(t+2). A bond with higher convexity benefits more when yields fall (price rises more than duration alone predicts) and loses less when yields rise (price falls less). Investors pay a premium for convexity — all else equal, a more convex bond is worth more.
DV01 (Dollar Value of an 01) is the dollar price change for a 1 basis-point (0.01%) yield move: DV01 = ModDuration × P × 0.0001. It is widely used to measure and hedge interest-rate exposure in fixed-income portfolios. The chart shows the curved price–yield relationship ±4 percentage points around the current YTM, with the current price marked.
Frequently asked questions
Duration gives a linear (first-order) approximation of price sensitivity: for small yield moves it is accurate, but for larger moves the convexity correction becomes significant. The full price change is approximately ΔP/P ≈ −ModDuration·Δy + ½·Convexity·Δy². For a 2% yield move, the convexity term can add 1–3% to the price change estimate, which is material for portfolio risk management.
A bond trades at par when its coupon rate equals the market yield. If the coupon rate exceeds the current YTM (bond is more generous than market rates), investors pay a premium above face value, so the price is above par. If the coupon rate is below the YTM, investors discount the bond below par. At maturity both premium and discount bonds converge to face value (pull-to-par).
Macaulay duration is the weighted-average time to receive a bond's cash flows, measured in years. Modified duration adjusts for the compounding frequency: ModDuration = MacDuration / (1 + YTM/m). Modified duration is the directly usable risk measure — it tells you the percentage price change per unit yield change. Macaulay duration has an intuitive interpretation (average wait for repayment) but is not directly a price-sensitivity measure.
TG we-Calculate Editorial Team. (2026). Bond Convexity Calculator — Duration & Convexity for Fixed-Income [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/bond-convexity-calculator
TG we-Calculate Editorial Team. "Bond Convexity Calculator — Duration & Convexity for Fixed-Income." TG we-Calculate. 2026. https://we-calculate.com/calculator/bond-convexity-calculator.
TG we-Calculate Editorial Team, "Bond Convexity Calculator — Duration & Convexity for Fixed-Income," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/bond-convexity-calculator
@misc{wecalculate_bond_convexity_calculator, title = {Bond Convexity Calculator — Duration & Convexity for Fixed-Income}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/bond-convexity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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