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.

摘要

我们使用基于强度的方法开发了具有部分提前还款风险的抵押转嫁证券的估值模型。对于给定抵押贷款池中的单一抵押合同，部分提前还款时间的提前还款额与未偿本金的比率用随机过程描述，提前还款的发生时间用Cox过程的跳跃时间建模。在这些条件下，我们分别得到了没有和有政权转换的抵押转嫁证券的估值公式。基于这些结果，我们还得到了服务机构从抵押池中收取的现金流量的预期现值和单抵押接触的估值公式。最后，我们给出了一些数值例子来研究参数如何影响估值。