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