Let's say I have a plain vanilla "broken date" swap (Annual fixed, 6m float) that I enter into today (10th Nov 20 for settle T+2, 12th Nov 20) and which ends on 16th August 2023. The swap is priced for zero PV. Let's say the fixed rate comes out at 1%.
The first fixed payment will be on 16th August 2021, and the first floating payment on 16th Feb 2021 (forgetting about good/bad days). Two rather basic questions:
What is the fixed cashflow on 16th August 21? Is it 1% or 1% * fraction of year(12th Nov 20 -> 16th Aug 21)?
What fix is used for the floating rate (an interpolated rate off today's fix(es), or a historical fix from 16-Aug-20), and again is it pro-rated by period fraction?
I should probably know the answer, and clearly there is a convention, as when trading broken-dates swaps there is never a discussion about what float rate to use (and dealers will all give very similar quotes for the fixed), but I'd be grateful to know what the convention is!