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B/c MC can project future probability with historical rates factored in. Mortgage loans suffer from low interest rate burn out, everybody who can refinance at the low interest rate already did, lowering it more doesn't do as much. The new prepayment rate is dependent on what the last i-rate was.

When you use a binomial, the probability of going up or down is not dependent on the last up or down move. It's the risk neutral probability.