Convexity is the second-order term that complements duration in rate sensitivity.

highlighted = computed this step

Convexity intuition

Duration is a tangent-line approximation around a point on the price-yield curve. Because the curve is convex, it always lies above that straight-line estimate: when yields fall, the actual price rises more than duration predicts; when yields rise, it falls less. Convexity is the correction for that gap. This is a descriptive risk shape, not a forecast.

convexity adds curvature correction Γ\text{convexity adds curvature correction } \Gamma