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?