Bond Parameters
Convexity Price Estimate
Convexity Analysis
Price Change Estimates
Exact vs. Estimated Prices
| Method | Estimated Price | Error vs Exact |
|---|---|---|
| Exact Repricing | — | — |
| Duration-Only | — | — |
| Duration + Convexity | — | — |
Formula Breakdown
Model Assumptions
- Fixed coupon bond (not floating rate or inflation-linked)
- Clean price calculation (excludes accrued interest)
- Periodic compounding matching payment frequency
- Flat yield curve (single YTM applies to all cash flows)
- No embedded options (not callable or putable)
For educational purposes. Not financial advice. Market conventions simplified.
What is Bond Convexity?
Bond convexity measures the curvature of the relationship between bond prices and yields. While duration provides a linear (first-order) approximation of how bond prices change when yields move, convexity captures the non-linear component that becomes increasingly important for larger yield shifts.
Mathematically, convexity is the second derivative of the bond price with respect to yield, scaled by the bond price. It is measured in units of years squared (years²).
Video Explanation
Video: Bond Convexity Explained
Duration vs. Convexity
Duration (First-Order)
- Linear approximation of price sensitivity
- Accurate for small yield changes (<50 bps)
- Always underestimates the true price for option-free bonds
- ΔP/P ≈ -Dmod × Δy
Convexity (Second-Order)
- Curvature correction to the duration estimate
- Essential for large yield changes (>50 bps)
- Always positive for option-free bonds (beneficial)
- Correction: + ½ × C × (Δy)²
When Does Convexity Matter?
The convexity adjustment is proportional to (Δy)², so it grows quadratically with yield changes. For a 50 basis point shift, the adjustment is 4 times larger than for a 25 basis point shift. This means:
- Small yield changes (<25 bps): Duration alone is usually sufficient
- Moderate changes (25–100 bps): Convexity noticeably improves accuracy
- Large changes (>100 bps): Convexity is essential; duration alone can produce significant errors
Bonds with higher convexity (longer maturity, lower coupon) benefit more from the convexity correction, and also provide a portfolio advantage: they gain more when yields fall than they lose when yields rise by the same amount.
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only and assumes option-free fixed coupon bonds with clean pricing (no accrued interest). Actual bond pricing involves additional factors including accrued interest, day count conventions, credit spreads, and embedded options. The duration and convexity approximations are most accurate for small-to-moderate yield changes. This tool should not be used for trading decisions.
Related Calculators
Course by Ryan O'Connell, CFA, FRM
Fixed Income Investing Course
Master fixed income investing from fundamentals to advanced strategies. Covers bond pricing, duration, convexity, yield curves, and interest rate risk management.
- Bond pricing, duration & convexity deep dives
- Yield curve analysis and term structure models
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- Hands-on exercises with real bond market data
