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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?

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    $\begingroup$ The baseline Vasicek model has constant instantaneous vol and implies a conditional rate distribution that is normal. When these assumptions are incorrect, interest rate options tend to show skew/smile pattern like equity options under Black-Scholes. There are more complicated extensions of the Vasicek model though. $\endgroup$
    – fes
    Commented Jul 8, 2022 at 8:39

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