How do I compute effective duration for a callable bond?

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AcadiFi · Accepted Answer

Effective duration uses the binomial tree to re-value the bond under parallel shifts in the benchmark curve up and down by a small amount (typically 25 bps each way). Formula: EffDur = (V_minus - V_plus) / (2 * V_0 * delta_y), where V_0 is the current price, V_plus is the price after rates rise by delta_y, V_minus is the price after rates fall by delta_y, and delta_y is the shift in decimal form. Procedure: (1) Price the bond today using the calibrated tree at an assumed OAS — get V_0, say 99.20. (2) Shift every node in the benchmark rate tree up by 25 bps, recompute the callable bond's value (call rules re-apply at each node), get V_plus = 97.85. (3) Shift down by 25 bps, revalue, get V_minus = 100.20. (4) Compute EffDur = (100.20 - 97.85) / (2 * 99.20 * 0.0025) = 2.35 / 0.496 = 4.74. Why lower than straight-bond duration? When rates fall, the straight bond's price would rise freely, but the callable bond's price is capped near the call price because more calls occur. This dampens the price increase (V_minus is pulled down from what a straight would show), flattening the price-yield curve. The straight 5-year bond might have EffDur of 4.4 while the callable is 3.1 — the call option shortens effective life. Near-par callables in low-vol environments have very low effective durations because they behave like short-dated bonds. Callables deep out of the money (rates far above coupon) have durations close to their straight-bond counterparts because calls are unlikely. Effective duration is not additive across positions in the same way modified duration is, but it is the appropriate risk metric for option-embedded instruments.

How do I compute effective duration for a callable bond?

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