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In finance convexity is a measure of the sensitivity of the price of a bond to changes in interest rates. It is related to the concept of duration.
Convexity is a measure of the curvature of how the price of a bond changes as the interest rate changes. Specifically, duration can be formulated as the first derivative of the price function of the bond with respect to the interest rate in question. Then the convexity would be the second derivative of the price function with respect to the interest rate.