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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?

Thanks!

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    $\begingroup$ They are not forecasting models, they are used for the valuation of options, which require an estimate of how much interest rates can change in the future (i.e. the volatilty, not the direction, of future interest rates). These models are used to crank out alternative paths for interest rates in the future, for the valuation of option-like interest rate derivatives. The expected path is not of any great interest for this purpose, it is 'what range of things could plausibly happen'. $\endgroup$ – Alex C May 7 '18 at 13:10
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    $\begingroup$ As @AlexC has explained, short-rate models are used to price interest rate derivatives, not to predict the future path of interest rates. They are most heavily used for pricing vanilla derivatives that depend on a single rate, instead of the whole curve; they are also used for pricing hybrid derivatives (e.g. a derivative that depends on a stock price and an interest rate). $\endgroup$ – Daneel Olivaw May 7 '18 at 13:29

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