Which of the following statements is (are) true with respect to the use of a Monte Carlo simulation model in order to value a mortgage-backed security?

I. Monte Carlo simulation models take into account past interest rates levels when determining prepayment rates.
II. All interest rate paths that are generated by the model must be able to correctly value all the various zero coupon Treasury bonds.
III. In general, a binomial model and a Monte Carlo simulation model should lead to the same valuation estimates for mortgage-backed securities.
IV. With a simulation model, if the interest rate projected for the end of the period is higher than interest rate the model began with, then a very low prepayment rate may be assumed.

Correct Answer: I only

I is true because Monte Carlo simulation models do take into account past interest rates levels in addition to current rate levels when determining prepayment rates. This is in contrast to binomial trees, which only examine the current interest rate levels in order to determine the likelihood of a call (or prepayment).

II is incorrect because all interest rate paths that are generated by the model must be able to correctly value all the various "on-the-run" Treasury bonds. We cannot use the zero-coupon bonds because they only have one cash flow. Instead, we need to test the paths on a Treasury that has cash flows at every junction, because we need this cash flow to discount it by the projected interest rate.

III is incorrect for the reasons spelled out in the explanation for statement I.

IV is incorrect because even if the interest rate projected for the end of the period is higher than interest rate the model began with, we really don't know what happened to interest rates in between the two points. If, it was the case that interest rates fell soon after the simulation began, than it is very possible that prepayment rates increased dramatically. So, even though the ending interest rate was higher, it did nothing to lower the prepayment rate previous to it.