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Option-Adjusted Duration (OAD)

Effective duration computed through the BDT tree — accounts for how embedded options change price sensitivity to rate moves.

OAD measures a bond's true interest rate sensitivity after accounting for embedded options. Computed by bumping the entire zero curve ±25bp, rebuilding the BDT tree at each bump, and repricing with the same OAS. The finite difference gives the duration that includes option exercise behavior. For callable bonds near the call price: OAD < modified duration (the call caps upside, reducing sensitivity). For putable bonds: OAD < effective duration (the put floors downside). For option-free bonds: OAD ≈ effective duration (no option exercise in tree). OAD is the correct duration measure for callable/putable bonds — using modified duration overstates interest rate risk.

Formula
OAD=−P+Δy−P−Δy2⋅Δy⋅P0\text{OAD} = -\frac{P_{+\Delta y} - P_{-\Delta y}}{2 \cdot \Delta y \cdot P_0}