Valuation of Fixed Rate Mortgages by Moving Boundary Approach

In this communication a moving boundary approach has been proposed to valuate a fixed rate mortgage contract which allows the mortgage holder to prepay the outstanding balance of the mortgage. This new method transforms the free-boundary problem into a monotonic sequence of moving boundary problems each of which can be solved by standard techniques. Illustrative examples demonstrate that the moving boundary approach is able to provide an accurate approximation to both the early exercise boundary and the contract value very efficiently. Furthermore, the approximate results can be systematically improved by the multi-stage approximation to the early exercise boundary.