Optimal refinancing strategy for a jump-diffusion mortgage rate model

Using a jump-diffusion process to characterize the mortgage rate, we consider the optimal refinancing strategy for interest-only mortgages. After transforming the two-dimensional refinancing problem into a one-dimensional optimization problem, we find that the optimal refinancing strategy is of a threshold type. The system of equations satisfied by the value function under the optimal refinancing strategy is also derived. Assuming that the jump sizes of the jump-diffusion process follow different distributions, we obtain the optimal refinancing threshold values and explicit expressions of the value function. Finally, some numerical results are provided to analyze the impact of some key parameters on the optimal refinancing strategy.