Why Vasicek on discrete lattice is a bad model for pricing American option on credit prepayment?

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Hasek

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I have an American option on a credit prepayment, i.e. the holder of the option can prepay the remaining credit if the interest rate falls below the initial strike. The pricing of this option was done on a discrete lattice (binomial tree) assuming that a risk-free part of the interest rate follows the one-factor Vasicek short rate model.

I was told that Vasicek on a tree is a terrible choice of model implementation and that one should either use Monte Carlo simulation with the Vasicek model or use the Hull-White model on a tree. I was also told that this is a bad practice in general to use one-factor models on trees. Can anyone elaborate on it?
 
I have not tried it myself because in general PDE/Finite different models are much better.

Having said that, lattice methods for American equity options are good.
Is it not a barrier option??

I was told that Vasicek on a tree is a terrible choice of model implementation and that one should either use Monte Carlo simulation with the Vasicek model or use the Hull-White model on a tree. I was also told that this is a bad practice in general to use one-factor models on trees. Can anyone elaborate on it?
Did you ask the 'teller' of this story WHY?
I think you need to be more precise.

Have a go at implementing it and come back with concrete feedback. HW is maybe better.
 
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