# Optimal refinancing strategy for mortgage rate with regime switching

Optimal refinancing strategy for mortgage rate with regime switching We investigate an optimal refinancing problem for an interest‐only mortgage, where the market mortgage rate is defined as the classical Black‐Scholes geometric Brownian motion with regime switching. We verify that the optimal refinancing strategy only depends on the quotient between the market mortgage rate and the borrowing rate. We show that the optimal refinancing strategy is of threshold type. By reducing the two‐dimensional optimal refinancing problem to a one‐dimensional problem, we obtain the system of equations that the function with respect to quotient satisfies. Analytic solutions are obtained in one‐ and two‐regime cases. Finally, we present some numerical results to illustrate the influence of the model parameters on the optimal refinancing strategy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Stochastic Models in Business and Industry Wiley

# Optimal refinancing strategy for mortgage rate with regime switching

, Volume 38 (1) – Jan 1, 2022
18 pages

/lp/wiley/optimal-refinancing-strategy-for-mortgage-rate-with-regime-switching-bfrplnDOmt

# References (50)

Publisher
Wiley
© 2022 John Wiley & Sons, Ltd.
ISSN
1524-1904
eISSN
1526-4025
DOI
10.1002/asmb.2652
Publisher site
See Article on Publisher Site

### Abstract

We investigate an optimal refinancing problem for an interest‐only mortgage, where the market mortgage rate is defined as the classical Black‐Scholes geometric Brownian motion with regime switching. We verify that the optimal refinancing strategy only depends on the quotient between the market mortgage rate and the borrowing rate. We show that the optimal refinancing strategy is of threshold type. By reducing the two‐dimensional optimal refinancing problem to a one‐dimensional problem, we obtain the system of equations that the function with respect to quotient satisfies. Analytic solutions are obtained in one‐ and two‐regime cases. Finally, we present some numerical results to illustrate the influence of the model parameters on the optimal refinancing strategy.

### Journal

Applied Stochastic Models in Business and IndustryWiley

Published: Jan 1, 2022

Keywords: geometric Brownian motion; mortgage; refinancing; regime switching