Given a 1-factor Hull-White interest rate model, what is the best way to estimate the mean reversion parameter that should be used?Presently I am calibrating to ATM Swaptions down the reverse diagonal of the swaption vol grid and so generating a piecewise constant Hull-White Vol curve. I'm unsure of the best way to determine the mean reversion and would be grateful for any suggestions,thanks,fred.

it depends on the product you are trying to price-V

1) Calib to ITT swaption like you did;2) Calib to caplets;3) Calib to the blend of above two.and that's it

I assume you are pricing bermuda swaption, thus the mean-reversion allows you to control correlations (aka auto-correlation) between short rate (or underlying swap rates) at different dates. Thus there are two ways to proceed :1) As suggested by Pat, you could manage a matrix of mean-reversion with respect to the 1st exercise of the bermuda and the tenor of the longest underlying swap.2) Second, you could tune the mean-rev to fit the auto-correlation of a multi-factor model.

For Bermudans, the best way is to calibrate mean reversion to the inter-temporal correlation of core swap rates (corr(S_i(T_i), S_j(T_j),i,j=1,...,N) as returned by a fully-calibrated BGM model-V

Hi I'd like to resurrect this thread. When calibrating HW mean reversion for Bermudans using a fully calibrated LMM what would be the recommended instrument set for LMM calibration? CMS spread options strike me as providing market information on terminal correlation for swap rates of different maturities that fix on the same date. A 1-F HW won't be able to capture this and it's not clear to me what this calibration would tell us about autocorrelation for Bermudans. We would seem to want market information for coterminal swaps fixing on different dates instead? Shy of using Bermudans themselves are there any other recommended instruments or strategies?Where there are no instruments beyond vanilla swaptions and caplets, is using historical correlation of forwards deemed at all reasonable for fitting mean reversion? I could think of three possible combinations:i) calibrate LMM forward rate vol functions to swaptions using the historical correlation of the forwards and then back out the corresponding inter-temporal correlations of the desired Bermduan's underlying swap rates to then fit the HW mean reversion.ii) use directly the historical correlation of the coterminal swaps of the desired Bermudan (with fixings occurring at their respective different dates) to fit the mean reversion inter temporal correlation.iii) use directly the historical correlation of the forwards that span the underlying swaps of the desired Bermduan fixing over different dates to fit the mean reversion.Any feedback greatly appreciatedThanks