I refer to MFM introduced by Hunt . These models can be seen a subset of interest rate market models. MFM allow us to describe the term structure elements using a set a functions of a low-dimensional Markov process (say 1 or 2).
This gives to the model the ability to calibrate fairly well and to capture the smile. Of course, due to limited number of risk factors can fail to capture the instantaneous correlation structures between rates. However, being low-dimensional, Markovian and relatively good with the smile it did not make it so popular yet.
If indeed this is true. What do you see as the reason? Why do people still prefer short rate modelling (maybe with stochastic vol) or even the path-dependent BGM?
Thank you in advance.