Home / Glossary / Option-Adjusted Convexity (OAC)

Option-Adjusted Convexity (OAC)

Second-order price sensitivity through the BDT tree — can be negative for callable bonds near the call price.

OAC measures the curvature of the price-yield relationship after option effects. Like OAD, it bumps the curve ±25bp, rebuilds the tree, and computes the second-order finite difference. For option-free bonds: OAC is always positive (prices are convex in yields). For callable bonds near the call price: OAC can be negative — as yields drop, the bond approaches the call price ceiling and price appreciation slows, creating negative convexity. This is a key CFA Level II concept: callable bonds exhibit negative convexity in the region where the call is in-the-money. For putable bonds: OAC is typically positive and higher than for option-free bonds.

Formula
OAC=P+Δy+P−Δy−2P0(Δy)2⋅P0\text{OAC} = \frac{P_{+\Delta y} + P_{-\Delta y} - 2P_0}{(\Delta y)^2 \cdot P_0}