A new type of prepayment model for use in the valuation of mortgage-backed securities is presented. The model is based on a simple axiomatic characterization of the prepayment decision by the individual in terms of a continuous time, discrete state stochastic process. One advantage of the stochastic approach compared to a traditional regression model is that information on the variability of prepayments is retained. This information is shown to have a significant effect on the value of mortgage-backed derivative securities. Furthermore, the model explains important path dependent properties of prepayments such as seasoning and burnout in a natural way, which improves fit accuracy for mean prepayment rates. This is demonstrated by comparing the stochastic mean to a nonlinear regression model based on time and mortgage rate information for generic Ginnie Mae collateral.