Bond Convexity Calculator
See how convexity improves the duration estimate when yields move by a larger amount.
Bond Convexity Calculator
Bond Price
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Modified Duration
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Convexity (years²)
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Price: Duration Only
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Price: Duration + Convexity
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Price: Full Repricing
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Actual price vs. duration and convexity approximations
Estimate vs. Full Repricing
| Method | New price (₹) | Change (₹) | Change (%) | Error vs exact (₹) |
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Error is the estimated price minus the exact repriced value.
Assumptions & method
- Method: convexity = [Σ PVₖ × k(k+1)] ÷ [Price × (1 + y/m)² × m²], where k is the period number and m is payments per year. The result is in years².
- Duration-only estimate: ΔP ≈ −ModDur × P × Δy. Duration + convexity estimate: ΔP ≈ −ModDur × P × Δy + ½ × Convexity × P × Δy².
- Yield-change assumption: a single, instantaneous, parallel shift applied to the yield to maturity, entered in percentage points. The resulting yield must stay at or above 0%.
- Full repricing recomputes the bond price at the new yield using the same cash flows, so it is the exact benchmark for the other two estimates.
- Price is computed on a coupon date with no accrued interest. Coupons are fixed and compounded at the coupon frequency; no call or default risk is modelled.
- Even duration + convexity is only a second-order approximation, so very large yield moves can still leave a small error.
Results are estimates based on the figures you enter. They are not guarantees and not financial advice.
What is bond convexity?
The relationship between a bond price and its yield is a curve, not a line. Duration is the slope of that curve at the current yield, so it is a good guide for small moves but drifts away as the move grows. Convexity measures how quickly the slope itself changes. Because the curve bends upward, a bond gains more from a fall in yield than it loses from an equal rise, and convexity captures that difference. Adding the convexity term to the duration estimate usually brings the result very close to the exact repricing, which you can confirm in the table. Higher convexity is generally welcome for holders, and it tends to be larger for long maturities and low coupons.