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.

This paper developed a unified framework for valuing non-performing loan (NPL)-backed securities under regime-switching macroeconomic conditions. The stochastic timing of NPL repayments were modeled by a Cox process with regime-dependent intensity, while investor risk aversion was incorporated through utility indifference pricing. Analytical solutions were obtained in a two-regime setting. Numerical results showed how risk aversion, repayment intensity, and macroeconomic state jointly affected the indifference price of NPL-backed securities.