Computational Economics

, Volume 52, Issue 2, pp 479–492 | Cite as

Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem

  • Dejun XieEmail author
  • Nan Zhang
  • David A. Edwards


This work studies a mortgage borrower’s optimal refinancing strategy, which is formulated as the solution to a stochastic minimization problem with contingent conditions. The problem is framed in a business economic environment where the underlying discounting factor and mortgage interest rate are assumed to follow a two-dimensional stochastic process of Vasicek type. A complete Monte Carlo algorithm is developed and implemented. This algorithm generates the optimal refinancing surface as a function of time and the risk-free rate. Numerical examples with financial implications are provided.


Mortgage refinancing Stochastic modeling Monte Carlo simulation Financial optimization 


  1. Barat, A., Donohue, K., Ruskin, H. J., & Crane, M. (2006). Probabilistic models for drug dissolution. Part 1. Review of Monte Carlo and stochastic cellular automata approaches. Simulation Modelling Practice and Theory, 14, 843–856.CrossRefGoogle Scholar
  2. Chen, C. H., Donohue, K., Yucesan, E., & Lin, J. (2003). Optimal computing budget allocation for Monte Carlo simulation with application to product design. Simulation Modelling Practice and Theory, 11, 57–74.CrossRefGoogle Scholar
  3. Chen, A., & Ling, D. (1989). Optimal mortgage refinancing with stochastic interest rates. Journal of the American Real Estate and Urban Economics Association, 17, 278–299.CrossRefGoogle Scholar
  4. Crotty, J. (2009). Structural causes of the global financial crisis: A critical assessment of the new financial architecture. Cambridge Journal of Economics, 33(4), 563–580.CrossRefGoogle Scholar
  5. Dunn, K., & McConnell, J. (1981a). A comparison of alternative models for pricing GNMA mortgage-backed securities. The Journal of Finance, 36, 471–483.CrossRefGoogle Scholar
  6. Dunn, K., & McConnell, J. (1981b). Valuation of GAMA mortgage-backed securities. The Journal of Finance, 36, 599–616.CrossRefGoogle Scholar
  7. Gan, S., Zheng, J., Feng, X., & Xie, D. (2012). When to refinance mortgage loans in a stochastic interest rate environment. Proceedings of the 2012 international multiconference of engineers and computer scientists, 2, March 14–16, Hong Kong.Google Scholar
  8. Lea, M. (1999). Prerequisites for a successful SMM: The role of the primary mortgage market. Inter-American Development Bank: Technical Paper Series.Google Scholar
  9. Lee, P., & Rosenfield, D. (2005). When to refinance a mortgage: A dynamic programming approach. European Journal of Operational Research, 166, 266–277.CrossRefGoogle Scholar
  10. Lo, C. F., Lau, C. S., & Hui, C. H. (2009). Valuation of fixed rate mortgages by moving boundary approach. Proceedings of the world congress on engineering, London.Google Scholar
  11. Longstaff, F. A. (2004). Optimal recursive refinancing and the valuation of mortgage-backed securities, NBER Working Paper No. 10422.Google Scholar
  12. Saunders, A., & Allen, L. (1999). Credit risk measurement: New approaches to value at risk and other paradigms. Hoboken: John Wiley.Google Scholar
  13. Saunders, A., & Allen, L. (2010). Credit risk management in and out of the financial crisis: New approaches to value at risk and other paradigms. Hoboken: John Wiley.CrossRefGoogle Scholar
  14. Vasicek, A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.CrossRefGoogle Scholar
  15. Xie, D., Chen, X., & Chadam, J. (2007). Optimal payment of mortgages. European Journal of Applied Mathematics, 3, 363–388.CrossRefGoogle Scholar
  16. Zheng, J., Gan, S., Feng, X., & Xie, D. (2012). Optimal mortgage refinancing based on Monte Carlo simulation. International Journal of Applied Mathematics, 42(2), 111–121.Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of FinanceSouth University of Science and Technology of ChinaShenzhenChina
  2. 2.Department of Computer Science and Software EngineeringXian Jiaotong-Liverpool UniversitySuzhouChina
  3. 3.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

Personalised recommendations