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Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem

Computational Economics volume 52, pages 479–492 (2018)Cite this article

Abstract

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.

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References

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dunn, K., & McConnell, J. (1981a). A comparison of alternative models for pricing GNMA mortgage-backed securities. The Journal of Finance, 36, 471–483.

    Article  Google Scholar 

  • Dunn, K., & McConnell, J. (1981b). Valuation of GAMA mortgage-backed securities. The Journal of Finance, 36, 599–616.

    Article  Google Scholar 

  • 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.

  • Lea, M. (1999). Prerequisites for a successful SMM: The role of the primary mortgage market. Inter-American Development Bank: Technical Paper Series.

    Google Scholar 

  • Lee, P., & Rosenfield, D. (2005). When to refinance a mortgage: A dynamic programming approach. European Journal of Operational Research, 166, 266–277.

    Article  Google Scholar 

  • 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.

  • Longstaff, F. A. (2004). Optimal recursive refinancing and the valuation of mortgage-backed securities, NBER Working Paper No. 10422.

  • Saunders, A., & Allen, L. (1999). Credit risk measurement: New approaches to value at risk and other paradigms. Hoboken: John Wiley.

    Google Scholar 

  • 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.

    Book  Google Scholar 

  • Vasicek, A. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.

    Article  Google Scholar 

  • Xie, D., Chen, X., & Chadam, J. (2007). Optimal payment of mortgages. European Journal of Applied Mathematics, 3, 363–388.

    Article  Google Scholar 

  • 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 

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Authors and Affiliations

  1. Department of Finance, South University of Science and Technology of China, Shenzhen, China

    Dejun Xie

  2. Department of Computer Science and Software Engineering, Xian Jiaotong-Liverpool University, Suzhou, China

    Nan Zhang

  3. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    David A. Edwards

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  1. Dejun Xie
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  2. Nan Zhang
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  3. David A. Edwards
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Correspondence to Dejun Xie.

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Xie, D., Zhang, N. & Edwards, D.A. Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem. Comput Econ 52, 479–492 (2018). https://doi.org/10.1007/s10614-017-9689-1

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  • DOI: https://doi.org/10.1007/s10614-017-9689-1

Keywords

  • Mortgage refinancing
  • Stochastic modeling
  • Monte Carlo simulation
  • Financial optimization