A new numerical method for pricing fixed-rate mortgages withprepayment and default options

Abstract

[Abstract] In this paper we consider the valuation of fixed-rate mortgages including prepayment and default options,where the underlying stochastic factors are the house price and the interest rate. The mathematical modelto obtain the value of the contract is posed as a free boundary problem associated to a partial differentialequation (PDE) model. The equilibrium contract rate is determined by using an iterative process. Moreover,appropriate numerical methods based on a Lagrange–Galerkin discretization of the PDE, an augmentedLagrangian active set method and a Newton iteration scheme are proposed. Finally, some numerical resultsto illustrate the performance of the numerical schemes, as well as the qualitative and quantitative behaviourof solution and the optimal prepayment boundary are presented