Abstract
This paper uses the stopping time of a stochastic process to value loans and mortgage-backed securities. We consider the implications of a borrower being faced with low interest rates or high home prices and how that scenario may influence a borrower to prepay the loan. Conversely, when the house price is below a certain value, the borrower has an option to default. By using the stopping time of a stochastic process as a proxy for loan termination, we can set a point a borrower desires to reach and determine when the stochastic process will arrive at pre-determined point. Once the point is reached, we will not consider that the stochastic process further. Thus, we use the pre-determined point (stopping time) of the stochastic process as a proxy for loan termination.