A term structure has a forward curve
So what is it that the short rate model is projecting exactly?
Why is it needed?
How are they different?
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1 Answer
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A yield curve is a deterministic function as set and seen at time T=0. One can project any short-term (e.g. 1 mth, 1 wk or 1 day) forward rates from the curve and they are deterministic.
A short rate model only projects the behaviour of the instantaneous short rate (again can be defined as any tenor). The forward rates from this model are generated from the model parameters and might not necessarily match the yield curve.
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$\begingroup$ I see! So in other words, the forward rates from the yield curve are deterministic and already known when given the yield curve is defined. The forward rate is "built-in" This is not necessarily the case with the short rate model, because you are picking parameters and projecting forward, so the output from the model will not be the same as the forward rate However, can you confirm that the projection from the short rate model and the forward curve are the same type of forecast? $\endgroup$– VVKK77Commented Mar 16, 2019 at 1:56
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$\begingroup$ yes, they will be the same forecast, explicitly if one assumes discounting for the yield curve (i refer to interbank swap rates) are accounted for, and the model parameters of the short rate are calibrated to the specified yield in mind. $\endgroup$– KiannCommented Mar 16, 2019 at 8:09
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$\begingroup$ @VVKK77, could you flag and accept my answer, if you find it helpful? Kind regards $\endgroup$– KiannCommented Mar 17, 2019 at 21:56
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