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I refer to MFM introduced by Hunt [2000]. 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.

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it's difficult to say that they are not popular. Some people definitely use them for live pricing. I'd say the real question is "why are they not popular in the academic literature"?

One answer would simply be that most the questions that arise in their use are ones of fiddliness which do not make good papers.

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