I am studying a previous post on how to build SOFR discount curve here Libor transition: Building SOFR discount curve
However, I struggle to understand the below formula
What is the reason of having LHS as 100 i.e. the Principal?
I understand that for normal IRS where float rate is determined by LIBOR and also discount factor is LIBOR then the PV of all floating leg CFs is 100 on each CF date. But here we are talking of different kind of Swap, where floar CF is determined not by LIBOR but the daily SOFR fixes during the interest period.
So, are they basically the same? Why?
Secondly, what if I am building SOFR curve not in the start day of Swap (or any float CF day)? How should I change above formula? Or, in the construction of SOFR curve, we will only consider SWAP instruments that starts on the construction date?
