Interest Rate Path Dependency

Why do we use a Monte Carlo simulation when interest rates are path dependent such as a HEL ABS and a binomial model when interest rates arent path dependent, such as a callable corporate bond? Tks!

Binomial model cannot be used as it has no way to incorporate prepayment burnout. If interest rates drop, then rise, then drop again, most of the people who will refinance, do it on the first drop. That means there are very few people left who will refinance the second time. There is no mechanism in the binomial framework to account for this, so Monte Carlo is used.

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.