I have come across the statement that the Vasicek model cannot be used to price skew / smile sensitive products: i.e. it cannot be calibrated to replicate a skew or smile. Why is that?
My guess is this: the instantaneous short rate can potentially have a time-varying volatility function (say time homogenous, if not a more sophisticated version): but at a fixed point in time, the vol function is only one-dimensional: so for any point in time, it can only be calibrated to one strike. Is this correct?