Bond Convexity Calculator

Calculate bond convexity and estimate price changes for large yield moves using duration + convexity adjustment. Includes effective convexity for callable bonds, positive vs negative convexity, and convexity benefit analysis.

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Convexity
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Modified Duration —
Duration-Only Price Change (±100bps) —
Convexity Adjustment (±100bps) —
Total Estimated Price Change (±100bps) —
Extended More scenarios, charts & detailed breakdown ▾
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Effective Convexity
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Convexity Type —
Professional Full parameters & maximum detail ▾
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Convexity & Duration

Convexity —
Modified Duration —

Price Change Estimates

Est. Price Change (+200bps) —
Est. Price Change (−200bps) —

Assessment

Convexity Assessment —

How to Use This Calculator

  1. Enter bond parameters: Face Value, Coupon Rate, YTM, Years to Maturity, and Payment Frequency.
  2. Convexity and Modified Duration are computed from the cash flow schedule.
  3. See estimated price changes for ±100 bps yield moves with the convexity adjustment.
  4. Use Effective Convexity tab for callable/putable bonds — input prices at ±100bp shocks.
  5. Use Duration vs Convexity Error tab to see how much duration underestimates for large moves.

Formula

Convexity = Σ[PV(CFt) × (t/freq) × ((t/freq) + 1/freq)] / (Price × (1+r)²)

ΔP/P ≈ −ModDur × Δy + 0.5 × Convexity × Δy²

Example

Example: 10-year bond, 5% coupon, 4.5% YTM, semi-annual. Modified Duration = 7.77, Convexity = 71.2. For +100bps yield move: Duration estimate = −7.77%. Convexity adjustment = +0.5 × 71.2 × (0.01)² = +0.356%. Total = −7.41% vs −7.77% from duration alone.

Frequently Asked Questions

  • Convexity is the second derivative of a bond's price with respect to yield. While Modified Duration gives a linear (first-order) estimate of price change, convexity adds the curvature correction. Full formula: ΔP/P ≈ −ModDur × Δy + 0.5 × Convexity × Δy². For large yield moves, this correction is significant.
  • Positive convexity means a bond's price rises more when yields fall than it falls when yields rise by the same amount — an asymmetry that benefits investors. Bullet bonds (no embedded options) always have positive convexity. Callable bonds can have negative convexity at low yields because the issuer may call the bond.
  • Embedded call options cause negative convexity. When yields fall, callable bond prices are capped (because the issuer will call the bond). Mortgage-backed securities also exhibit negative convexity due to prepayment risk — homeowners refinance when rates drop, cutting off your high-coupon cash flows.
  • For a 10-year bond with convexity of 100 and a 100 bps yield move: Convexity adjustment = 0.5 × 100 × (0.01)² = 0.5% — significant but small. For a 200 bps move: 0.5 × 100 × (0.02)² = 2.0% — very material. Duration alone would severely underestimate the price gain for large rate decreases.
  • Convexity (analytical) is computed from the bond's cash flows using a formula. Effective Convexity = (P+ + P− − 2P₀) / (P₀ × Δy²) uses actual bond prices at shocked yields, capturing embedded option effects. Use effective convexity for callable bonds, putable bonds, and MBS.

Related Calculators

⏳ Bond Duration Calculator 📊 YTM Calculator 📊 Bond Yield Calculator 💰 Present Value Calculator
Sources & References (5) ▾
  1. Handbook of Fixed Income Securities — Frank Fabozzi — McGraw-Hill
  2. CFA Institute — Fixed Income Vol 5: Interest Rate Risk and Return — CFA Institute
  3. Bond Convexity — Investopedia — Investopedia
  4. MSCI Fixed Income Analytics — MSCI
  5. Vanguard — Bond Duration and Convexity — Vanguard