Anyone knows why the OIS leg for basis swaps pays the average rate instead of the geometric average compounding rate as expected for a regular OIS swap leg?
As far as I know, it's a market convention. The two products, namely OIS swap (fixed vs floating) and Fed Fund Libor basis swap, are developed differently, so they follow different conventions.
My only guess is that it's because of the difference in maturity and period: OIS swap is typically a single-period swap (i.e. zero coupon swap) on short-end (< 2 yrs) while FF Libor basis swap is multiple period swap on long-end (> 2 yrs). The geometric compounding is for mimicking the daily reinvestment, so it makes sense for the single period. However, the daily reinvestment is not in line with multiple period swap because the notional is reset at every period, so you don't have to stick to the geometric compounding. In fact, arithmetic averaging is a much simpler computing choice to layman.
$\begingroup$ Weirdly enough though it doesn't seem to be the case for EUR and GBP ( using the same geometric average method for OIS and Basis swaps). $\endgroup$– sw89Mar 1, 2017 at 12:03
$\begingroup$ Good to know that. Then, I can only say it's just a convention. Although geometric compounding is daunting, it's simpler in mathematical modelling because it's a natural numeraire of Fed Fund. For arithmetic averaging, you need to compute the convexity correction, which is lots of headache. $\endgroup$– jChoiMar 1, 2017 at 12:07