Estimation of LIBOR 3M periods if the period is not exactly 3M months

Question

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 1

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.