Let's suppose our swap has a structured coupon which depends on two CMS swap rate: 5Y and 2Y, both with 6m frequence. Our payment dates are T1<T2<T3<...<T20. e.g. 3m frequence. Today is T0<T1. At each fixing date, the two swap rates are observed which is a CMS rate and start at the fixing dates. And we can calculate the coupon. My problem is how to simulate these two rates.I know usually we can use so-called T1-forward measure where the two CMS rates are under the same measure, and we are able to simulate them up to time T1. But after T1 has been simulated and the coupon has been computed, next fixing date is T2, should I change to T2-forward measure and simulate the rates at T2? Is that inconsistent?The underlying forward rate process can be HJM or LFM.Advise?Thanks.

I am a stupid trader and not a quant, but the payments look independent of each other from one period to the next (no path dependence). So you can do a "long jump" and simulate them all independently for each period and in their own measure and discount the results back to today. So you simulate the 5y and 2y joint distribution for T1, construct your payoff, discount it. Then simulate the 5y and 2y distribution in the 2nd period from T1 to T2. The starting point for that 2nd period does not depend on where each path in the first period ended, so you can just start the simulation at today's forwards. And so on. If this is wrong please let me know and accept my apologies in advance.

Yap. I actually thought about what you said. If I discount them all to today from (T1,T2 ...), I can add them up to get the pv of this structured coupon. The problem is if I have 20 fixing dates, and for each one we have to do 10,000 simulation paths, the computation time would not be nice.Another problem is that if I have a bermuda option on this swap with the exercise dates being the fixing dates, how could I use Longstaff & Schwartz or Andersen method to price it?Thanks.

You can simulate the option in a T20 forward measure. Then for each payoff for t < T20, you bring it to T20 by dividing the payoff by the simulated P(t,T20)'s.The resulting payoffs can be discounted by P(0,T20).

20*10,000 simulations are really not that big a deal in my opinion.how are you going to simulate joint distribution(if bivariate normal then where are you getting correlation or term structure of correlation and vols) i think thats more important.swaption on this is a later step.