I know in order to price Bermudan swaption, the joint distribution of co-terminal swap rates at their setting dates is important. We would want to capture the correct marginal distribution and terminal correlation of co-terminal swap rates. The marginal distribution is relatively easy to be recovered by calibrating to the co-terminal swaption market price. My question is how to calibrate to the terminal correlation of swap rates in ONE-FACTOR LIBOR market model (I know it's not desirable to use such model to price bermudan, but this is just a question). Or no need to fit to terminal correlation, but just fit to part of swaption matrix? Thanks.

Pricing Bermudans in one factor models is quite common, so I would not say that "it is not desirable". I (highly!) recoomend this book that has a lot of info on calibration strategies for Bermudans.some people use a shortcut and calibrate the model to the inverse diagonal of the swaption matrix (co-terminal swaptions) and the first column (caplets); this calibration captures (some) information on terminal correlations that you needVladimir