The OAS Approach and the Martingale Measure for Mortgage Prepayment

The option-adjusted spread (OAS) is a standard measure in evaluation of mortgage-backed securities. In calculating the OAS, a prepayment model is incorporated to generate prepayment cashflows, however, no attention has been paid to a prepayment process and its associated probability measure. To illustrate the situation we examine two categories of prepayment models, the proportional hazards and the Poisson regression models. We formulate prepayment processes by point processes and find constraints on the point processes under which these prepayment models are reproduced. The prepayment rate is specified by the intensity of the point processes, and the intensity depends on a probability measure. We give warning of implicitly adpopting the real measure in the OAS approach.