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ΔPP=−DEΔy+12CEδy2 \frac{ \Delta P } { P } = - D_E \Delta y + \frac{1}{2} C_E \delta y ^ 2 PΔP=−DEΔy+21CEδy2
where DE,CED_E, C_E DE,CE are the effective duration and effective convexity of the bond
Dollar Convexity C=∂2P∂y2 C = \frac{ \partial^2 P } { \partial y^2 } C=∂y2∂2P
Effective Convexity CE=CP C_E = \frac{C}{P} CE=PC
Approximate convexity CE≈−P(y+Δy)−2P(y)+P(y−Δy)P(y)Δy2 C_E \approx - \frac{ P ( y + \Delta y ) - 2 P(y) + P ( y - \Delta y ) } {P(y) \Delta y ^ 2 } CE≈−P(y)Δy2P(y+Δy)−2P(y)+P(y−Δy)
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