In vanilla swap, the FL payments is fixed on one date and paid on the next reset date. So the next payment is known. However, the payment after that is not known. What would be the best estimate of that, mathematically?
Applying Markov property to bond price, expected price will not change. Calculate next to next payment from the next known payment along with forward rate at the next reset period. It seems to be simple.
I am looking for a more mathematically correct way to approach this, if any.