Reconciling Floating-Leg Duration with Swap DV01
Summary
The document considers why bump-and-reprice calculations can assign substantial duration to an interest rate swap’s floating leg, even though a common bond-style approximation treats that leg as having near-zero duration. Shifting the forward curve changes projected reset rates across future accrual periods, creating sensitivity that the simplified assumption omits.
The response says total swap duration can still be similar under both approaches because the fixed leg’s sensitivity balances the difference, leaving comparable net interest-rate exposure. This is a conceptual explanation rather than a derivation: it gives no equations, numerical example, or precise bump conventions. In practice, comparisons depend on how projection and discount curves are shocked, and the near-zero floating-leg rule is an approximation whose suitability may vary with reset frequency and instrument details.
Key ideas
- A parallel forward-curve bump changes projected rates across future floating-leg resets.
- That effect can make the floating leg appear to have significant duration in a bump-and-reprice calculation.
- The fixed leg can offset differences in leg-level sensitivity, leaving similar net swap sensitivity.
- The near-zero floating-leg duration assumption is a simplifying convention, not a universal description of each leg.
Tags
Full text
# Difference between DV01 and Macaulay duration for floating leg of IRS # Difference between DV01 and Macaulay duration for floating leg of IRS I’m building a pricing library for interest rate swaps and using numerical differentiation (bumping both the forward projection and discount curves) to compute DV01. As a sanity check, I compared this to a bond-style Macaulay duration for the fixed leg under the usual assumption that the floating leg has near-zero duration—especially for frequent-reset swaps like OIS. However, in my bump-and-reprice approach, the floating leg appears to have a large duration (often larger than the fixed leg’s, in particular for short-dated or low-rate swaps), which contradicts the standard assumption that the floating leg’s duration is negligible. Yet, both methods still yield very similar overall swap durations. One reason for the duration on the floating leg could be the compounding effect of the forward projections. By bumping the whole forward curve, the forward projections are compounded over the accrual periods which is not wholly offset by a bumped discount factor. But still, I am struggling to understand how these two seemingly conflicting treatments of the floating leg’s duration reconcile, and why do they produce the same total swap duration despite their different assumptions? Thank you for your help! ## Answer by João (score 1) https://quant.stackexchange.com/a/82093 Even tho the floating leg shows a larger duration in bump (because shifting the entire forward curve impacts all future reset rates, thus leading to a compounding effect), the total swap duration remains approximately the same This happens because the fixed leg adjusts, and it balances out the difference > But still, I am struggling to understand how these two seemingly conflicting treatments of the floating leg’s duration reconcile, and why do they produce the same total swap duration despite their different assumptions? because both of them "produce" the same total duration since it´s same net int. rate sensitivity Interest Rate Swaps and Their Derivatives from Amir Sadr fixed income from F. Fabozzi are both nice readings
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.