Optimal mortgage refinancing based on Monte Carlo simulation

The pricing of mortgages in the context of stochastic interest rate plays an important role for financial management. The contributing factors impacting the mortgage contract value have been explored by abundant literatures. However, the market players anticipate a systematic but low-cost approach to minimize the net present value of the payment streams by taking advantage of Refinancing, for instance. This paper focuses on finding a desirable Refinancing time for mortgage borrowers to minimize the total payment in a stochastic interest rate environment. The underlying interest rate is assumed to follow a stochastic process with mean-reverting property, the setting of which is broad enough to accommodate a large spectrum of market realities. Two types of commonly adopted mortgage balance settlement schemes are analyzed and compared to ensure the applicability of our study. Our numerical algorithm is validated with with varying samplings, leading to several interesting characteristics pertaining to the optimal mortgage Refinancing period. As one of the applications, we obtain the optimal boundary conditions for the value of the mortgage contract for all time before the expiry of the contract. Our approach and algorithm provide cost effective and easy to use financial tools for both institutional and individual property investors.