Bond Convexity

$\frac{ \Delta P } { P } = - D_E \Delta y + \frac{1}{2} C_E \delta y ^ 2$

where $D_E, C_E$ are the effective duration and effective convexity of the bond

Dollar Convexity $C = \frac{ \partial^2 P } { \partial y^2 }$

Effective Convexity $C_E = \frac{C}{P}$

Approximate convexity $C_E \approx - \frac{ P ( y + \Delta y ) - 2 P(y) + P ( y - \Delta y ) } {P(y) \Delta y ^ 2 }$