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Closed‐Form Mortgage Valuation Using Reduced‐Form Model

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  • Szu‐Lang Liao
  • Ming‐Shann Tsai
  • Shu‐Ling Chiang

Abstract

Valuing mortgage‐related securities is more complicated than valuing regular defaultable claims due to the borrower's prepayment behavior as well as the possibility of default. Some researchers use a structural‐form model to obtain the closed‐form formulas for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise. As an alternative, the reduced‐form model developed in this article is able to value the mortgage without setting boundary conditions, and it can thereby accurately handle the multidimensional space of correlated state variables. The purpose of this article is to derive a closed‐form solution of the mortgage valuation equation under a general reduced‐form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses. An implementation procedure for the model is also provided to demonstrate how the valuation framework can be utilized in practical applications.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:reesec:v:36:y:2008:i:2:p:313-347
    DOI: 10.1111/j.1540-6229.2008.00215.x
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    2. Shu Ling Chiang & Ming Shann Tsai & Shan Jiang, 2021. "The Influences of Foreclosure Factors on the Value, Yield, Duration and Convexity of a Mortgage," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 49(S2), pages 361-394, September.
    3. 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.
    4. 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.
    5. 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.
    6. Shu-Ling Chiang & Ming-Shann Tsai, 2010. "Pricing a defaultable bond with a stochastic recovery rate," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 49-58.
    7. 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.
    8. Chuang-Chang Chang & Hsiao-Wei Ho & Henry Hongren Huang & Yildiray Yildirim, 2024. "A reduced-form model for lease contract valuation with embedded options," Review of Quantitative Finance and Accounting, Springer, vol. 62(2), pages 841-864, February.

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