Optimal refinancing strategy for a jump-diffusion mortgage rate model

Congjin Zhou; Yinghui Dong; Wanrong Mu; Congjin Zhou; Yinghui Dong; Wanrong Mu

doi:10.3934/math.20251251

AIMS Mathematics

2025, Volume 10, Issue 12: 28436-28450. doi: 10.3934/math.20251251

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Research article

Optimal refinancing strategy for a jump-diffusion mortgage rate model

1.
School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China
2.
School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China

Received: 22 October 2025 Revised: 21 November 2025 Accepted: 28 November 2025 Published: 03 December 2025
MSC : 91B70, 60G40

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.
- mortgage,
- refinancing strategy,
- jump-diffusion process,
- threshold type
Citation: Congjin Zhou, Yinghui Dong, Wanrong Mu. Optimal refinancing strategy for a jump-diffusion mortgage rate model[J]. AIMS Mathematics, 2025, 10(12): 28436-28450. doi: 10.3934/math.20251251

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Abstract

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.

References

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