As far as I understand, a compounded swap rolls up individual payments into one final payment which becomes

$$ V(T) = N\prod_{i=1}^n(1+d_iL_i) $$

where $d_i$ is the day fraction for period $t_i$ to $t_{i+1}$ and $L_i$ is the index for the same period.

Now, to value this we need to calculate the expectation of $V(T)$ under some appropriate numeraire and measure, but we are dealing with products of various $L_i$'s which are, in general, not mutually independent, so it's not a simple matter of replacing with them forwards.

How is this then done? An internet search only revealed simple formulas using forwards. A good reference text would be welcome.