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The Valuation at Origination of Mortgages with Full Prepayment and Default Risks

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Listed:
  • Congjin Zhou

    (Suzhou University of Science and Technology)

  • Guojing Wang

    (Soochow University)

  • Yinghui Dong

    (Suzhou University of Science and Technology)

  • Pin Wang

    (Soochow University)

Abstract

We investigate the valuation problem of a mortgage contract with full prepayment and default risks using the reduced-form model with regime switching. The hazard rates of full prepayment and default are specified as linear functions of the risk-free interest rate and house prices, respectively, which are characterized by Ornstein-Uhlenbeck processes with regime switching. To derive the explicit valuation formula, we derive the distribution of the number of transitions for two-state Markov processes in finite time and the conditional joint probability density function of transition times using the uniformization technique. Finally, we analyze the effect of parameters on the valuation of the mortgage.

Suggested Citation

  • Congjin Zhou & Guojing Wang & Yinghui Dong & Pin Wang, 2024. "The Valuation at Origination of Mortgages with Full Prepayment and Default Risks," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-26, June.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:2:d:10.1007_s11009-024-10081-2
    DOI: 10.1007/s11009-024-10081-2
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    1. John Y. Campbell & João F. Cocco, 2015. "A Model of Mortgage Default," Journal of Finance, American Finance Association, vol. 70(4), pages 1495-1554, August.
    2. Christopher L. Foote & Paul S. Willen, 2018. "Mortgage-Default Research and the Recent Foreclosure Crisis," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 59-100, November.
    3. Chang, Chia-Chien, 2014. "Valuation Of Mortgage Insurance Contracts With Counterparty Default Risk: Reduced-Form Approach," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 303-334, May.
    4. Leung, Charles, 2004. "Macroeconomics and housing: a review of the literature," Journal of Housing Economics, Elsevier, vol. 13(4), pages 249-267, December.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Szu‐Lang Liao & Ming‐Shann Tsai & Shu‐Ling Chiang, 2008. "Closed‐Form Mortgage Valuation Using Reduced‐Form Model," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 36(2), pages 313-347, June.
    7. Deng, Yongheng & Gu, Quanlin & He, Jia, 2021. "Reinforcement learning and mortgage partial prepayment behavior," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    8. Chiang, Shu Ling & Yang, Tyler T. & Tsai, Ming Shann, 2016. "Assessing mortgage servicing rights using a reduced-form model: Considering the effects of interest rate risks, prepayment and default risks, and random state variables," Journal of Housing Economics, Elsevier, vol. 32(C), pages 29-46.
    9. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    10. Bhattacharya, Arnab & Wilson, Simon P. & Soyer, Refik, 2019. "A Bayesian approach to modeling mortgage default and prepayment," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1112-1124.
    11. Michael J. Brennan & Eduardo S. Schwartz, 1985. "Determinants of GNMA Mortgage Prices," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 209-228, September.
    12. Green, Jerry & Shoven, John B, 1986. "The Effects of Interest Rates on Mortgage Prepayments," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 18(1), pages 41-59, February.
    13. Dunn, Kenneth B & McConnell, John J, 1981. "Valuation of GNMA Mortgage-Backed Securities," Journal of Finance, American Finance Association, vol. 36(3), pages 599-616, June.
    14. Adriana Ocejo, 2015. "Asian option as a fixed-point," Papers 1510.08161, arXiv.org, revised Apr 2018.
    15. Donald Gross & Douglas R. Miller, 1984. "The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes," Operations Research, INFORMS, vol. 32(2), pages 343-361, April.
    16. Peimin Chen & Igor Kozhanov & Peng Liu & Chunchi Wu, 2021. "Commercial Mortgage‐Backed Security Pricing with Real Estate Liquidity Risk," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 49(S2), pages 490-525, September.
    17. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    18. Ming Shann Tsai & Shu Ling Chiang, 2015. "A General Pricing Model for a Mortgage Insurance Contract Considering the Effects of Multivariate Random Variables on Termination Probabilities and Loss Rate," Housing Policy Debate, Taylor & Francis Journals, vol. 25(2), pages 289-307, April.
    19. Ambrose, Brent W & Sanders, Anthony B, 2003. "Commercial Mortgage-Backed Securities: Prepayment and Default," The Journal of Real Estate Finance and Economics, Springer, vol. 26(2-3), pages 179-196, March-May.
    20. Christopher Mayer & Karen Pence & Shane M. Sherlund, 2009. "The Rise in Mortgage Defaults," Journal of Economic Perspectives, American Economic Association, vol. 23(1), pages 27-50, Winter.
    21. Tsai, Ming-Shann & Liao, Szu-Lang & Chiang, Shu-Ling, 2009. "Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks," Journal of Housing Economics, Elsevier, vol. 18(2), pages 92-103, June.
    22. repec:bla:jfinan:v:44:y:1989:i:2:p:375-92 is not listed on IDEAS
    23. Apaar Sadhwani & Kay Giesecke & Justin Sirignano, 2021. "Deep Learning for Mortgage Risk [The Subprime Virus]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 313-368.
    24. Schwartz, Eduardo S & Torous, Walter N, 1992. "Prepayment, Default, and the Valuation of Mortgage Pass-through Securities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 221-239, April.
    25. Stanton, Richard, 1995. "Rational Prepayment and the Valuation Mortgage-Backed Securities," The Review of Financial Studies, Society for Financial Studies, vol. 8(3), pages 677-708.
    26. Kau, James B. & Keenan, Donald C. & Muller III, Walter J. & Epperson, James F., 1995. "The Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment," The Journal of Real Estate Finance and Economics, Springer, vol. 11(1), pages 5-36, July.
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