||Using a discrete time approach, this paper presents a no-arbitrage pricing formula for MBSs (mortgage-backed securities), and taking into the heterogeneity of a mortgage pool, proposes a specific model for MBS prices that describes the so-called burnout phenomenon of prepayments due to refinance, sale of houses for mortgage, and default. This is a generalized version of Kariya and Kobayashi (2000) in which only refinance is considered for prepayment. The heterogeneity of the mortgage pool is expressed by different response functions of mortgage borrowers to the changes of interest rates and the price changes of equities or houses. Numerical examples for pricing MBSs are demonstrated together with certain specifications of interest model and price model. An estimation procedure is provided based on a recursive least squares method. The discrete time no arbitrage theory is discussed in Appendix.