An Optimal Mortgage Refinancing Strategy with Stochastic Interest Rate

This article puts forward a framework for assessing the optimal refinancing strategy in continuous time when the interest rate is stochastic and follows a Vasicek model. The optimal refinancing time is obtained by minimizing the conditional expectation of the discounted total payment. A moment generating function is used to derive a closed-form approximation to the refinancing function with infinite maturity under the Vasicek model. The approximation is studied both analytically and numerically. The results indicate three different types of behaviour in the refinancing function, depending on the underlying parameters in the model. Two types indicate optimal refinancing in finite time. We outline a strategy by which a borrower can continually evaluate whether to refinance. By providing a systematic way to evaluate the likelihood of refinancing, these results should be of interest to those trading mortgage-backed securities.