What is mathematically rigorous way to estimate floating swap cash flow in the future?

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.

• Are you talking about estimating the dynamics of the forward rates? – HelloWorld Nov 9 '15 at 4:34
• Yes, that is what I am thinking of. – user12348 Nov 10 '15 at 4:02
• The Libor over a later period is a random variable. The best estimate, in $L^2$ sense, is the expectation for today or the conditional expectation for a day after today. – Gordon Nov 10 '15 at 15:13
• Estimating the dynamics of forward rates is an interesting problem, and very important for the pricing of swaptions and caps etc., however it does not play any role in the accepted method for pricing swaps. For this the forward rates can just be read-off the current forward curve and no-arbitrage does the rest. – noob2 Nov 27 '15 at 14:44
• Do you really want to model the dynamics of do you want to have a market consistent estimate of the floating payments in the future of the swap? In the latter case if is the forward rate that applies to the period. – Ric Sep 30 '16 at 7:08