Just venturing into quantitative finance and studying short rate models (Vasicek, CIR, Hull-White etc.). Wanted to ask a very simple intuitive question. How would a practitioner use these models? I understand that they are used to simulate the future price of the short rate because the time series generated by these models have properties similar to those observed in historical rate time series - by running Monte Carlos with these models you can construct a distribution for the path of the short rate. Fine. But you could also write an ARMA (or some variant including GARCH) model which has the same properties (mean reversion, known variance) and produced forecasts which are the same as the expectation of the short rate model. My questions are:
Am I correct in thinking of the short rate models purely as an approximation/description tool and NOT as forecasting models (like VAR, for instance)? This seems intuitive as there is no information in short rate models except for the history of the time series.
How would a practitioner use these models to do something useful?