Effective Convexity

Effective convexity measures the curvature of the price-yield relationship for bonds with embedded options, accounting for how the option changes cash flows at different yield levels. For option-free bonds, effective convexity ≈ standard convexity (always positive). For callable bonds near the call price: effective convexity can be negative — as yields drop, the price appreciation is capped by the call price, creating a concave (negative-convex) region. This is the key risk of callable bonds: investors lose the upside convexity in a falling-rate environment. For putable bonds: effective convexity is higher than equivalent option-free bonds — the put provides a floor on price decline, enhancing convexity. Computed via the OAS-adjusted BDT tree (same methodology as OAD/OAC).