Mathematical analysis of obstacle problems for pricing fixed-rate mortgages with prepayment and default options

In this paper, we address the mathematical analysis of a partial differential equation model for pricing fixed-rate mortgages with prepayment and default options, where the underlying stochastic factors are the house price and the interest rate. The mathematical model is posed in terms of a sequence of linked complementarity problems, one for each month of the loan life, associated with a uniformly parabolic operator. We study the existence of a strong solution to each one of the obstacle problems.