Convexity measures the curvature of the price-yield relationship of a bond. While duration provides a linear approximation of how price changes with yield, convexity captures the fact that the actual relationship is curved. The formula is: Convexity = ∑ [t(t+1) × PV(CF_t)] / [P × (1+y)² × freq²]. A higher convexity means the price-Yield Curve bends more, making the duration approximation less accurate for large yield changes.

The total estimated price change combines both measures: ΔP/P ≈ -Duration × Δy + ½ × Convexity × (Δy)². The convexity term is always positive (for standard bonds), which means it works in the investor's favor: prices rise more than duration predicts when yields fall, and prices fall less than duration predicts when yields rise. This asymmetry is why investors value convexity.

Bonds with higher convexity are generally more desirable because they offer better protection against rate increases and greater price gains when rates decline. Zero-coupon bonds have the highest convexity for a given maturity because all cash flow is concentrated at maturity. Callable bonds exhibit negative convexity at lower yields because the call option caps the upside price potential.