Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem

This work studies a mortgage borrower’s optimal refinancing strategy, which is formulated as the solution to a stochastic minimization problem with contingent conditions. The problem is framed in a business economic environment where the underlying discounting factor and mortgage interest rate are assumed to follow a two-dimensional stochastic process of Vasicek type. A complete Monte Carlo algorithm is developed and implemented. This algorithm generates the optimal refinancing surface as a function of time and the risk-free rate. Numerical examples with financial implications are provided.