Convexity Adjustments for Short LIBOR Swap Periods
Summary
The note asks whether a final swap accrual period shorter than a standard three-month LIBOR tenor needs a convexity adjustment. It explains that a theoretical adjustment can arise when the LIBOR end date differs from the swap coupon payment date: the forward rate is a martingale under a measure tied to the LIBOR end date, while the coupon value is evaluated under a measure tied to its payment date.
The response says that this adjustment also exists for standard swaps with upfront resets, but is usually very small when the dates differ by only a few days and can generally be ignored in practice. It also notes that using the same pricing code to bootstrap projection curves and value standard swaps can further reduce practical inconsistency. The discussion is qualitative and gives no formula, numerical estimate, or treatment of larger date gaps, so it does not establish when the approximation may become material.
Key ideas
- A mismatch between the LIBOR end date and coupon payment date creates a theoretical measure-related convexity adjustment.
- The adjustment can occur even in standard swaps with upfront resets.
- When the date mismatch is only a few days, the effect is described as very small and often safe to ignore.
- Consistent pricing methods for curve bootstrapping and swap valuation can help limit practical inconsistencies.
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Full text
# Estimation of LIBOR 3M periods if the period is not exactly 3M months # Estimation of LIBOR 3M periods if the period is not exactly 3M months When generating dates of interest rate swaps, even without stub periods, we sometimes end up with periods that are less than 3 months (say 87 day). In that case do we have to apply any kind of convexity adjustment? So say my swap has the last period with the following characteristics: - Reset date (aka Fixing Date): 31-March-2019 - Calculation Start Date (+2 Business Day): 06-Apr-2021 - Calculation End Date (= Maturity of the deal): 02-Jul-2021 Now a normal USD LIBOR 3M period would with the following characterists: - Reset date (aka Fixing Date): 31-March-2019 - Calculation Start Date (+2 Business Day): 06-Apr-2021 - Calculation End Date (+ 3 months modfol NYB calendar): 06-Jul-2021 In that case, when estimating my swap period floating rate, should I apply a convexity adjustment? Is it for the same reason explained in https://quant.stackexchange.com/a/43218/31714 Thanks! ## Answer by Antoine Conze (score 0, accepted) https://quant.stackexchange.com/a/49515 In theory there even for standard swaps (reset upfront) there is a convexity adjustement as soon as the libor end date is different than the swap coupon payment date (because the forward libor is martingale under the libor end date measure and the swap coupon PV is computed using expectation under the coupon date measure), but in practice with only a few days difference it would be very small and can be safely ignored. Even more if the same pricing code is used both to bootstrap projection curves and to value standard swaps.
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