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I found some very interesting (promo?) slides from SocieteGenerale discussing WHY the Libor Market Model LMM [aka BGM/J, an instance of HJM] has become so popular, despite its significant imperfections.
But are we fooling ourselves that we can still put “the wrong number in the wrong formula to get the right price”?
I think they miss the point, basically you need some parameters to make a good model fit the environment [to paraphrase Dermans definition of useful ‘model’ is that it allows you to price something from other, somehow related, market observables]. Sure, you need several parameters to get enough flexibility to calibrate to the market.