Valuation of mortgage pass-through securities with partial prepayment risk

Abstract

We develop a valuation model for mortgage pass-through securities with partial prepayment risk using an intensity-based approach. For the single mortgage contract in a given pool of mortgage loans, the ratio of prepayment amount to outstanding principal at partial prepayment time is described by a stochastic process, and the occurrence time of prepayments is modeled by jump time of a Cox process. Under these conditions, we get the valuation formulas of mortgage pass-through securities without and with regime switching, respectively. Based on these results, we also obtain the expected present value of the cash flow charged by the service agency from the mortgage pool and the valuation formula of the single mortgage contact. Finally, we give some numerical examples to study how parameters affect the valuation.