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Analyzing yield, duration and convexity of mortgage loans under prepayment and default risks

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  • Tsai, Ming-Shann
  • Liao, Szu-Lang
  • Chiang, Shu-Ling
Abstract
In this article, we construct a general model, which considers the borrower's financial and non-financial termination behavior, to derive the closed-form formula of the mortgage value for analyzing the yield, duration and convexity of the risky mortgage. Since the risks of prepayment and default are reasonably expounded in our model, our formulae are more appropriate than traditional mortgage formulae. We also analyze the effects of the prepayment penalty and partial prepayment on the yield, duration and convexity of a mortgage, and provide lenders with an upper-bound for the mortgage default insurance rate. Our model provides portfolio managers a useful framework to more appropriately appraise the mortgage and more effectively hedge their mortgage holdings. From the results of sensitivity analyses, we find that higher interest-rate, prepayment and default risks will increase the mortgage yield and reduce the duration and convexity of the mortgage.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jhouse:v:18:y:2009:i:2:p:92-103
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    References listed on IDEAS

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    Cited by:

    1. Timothy Besley & Neil Meads & Paolo Surico, 2013. "Risk Heterogeneity and Credit Supply: Evidence from the Mortgage Market," NBER Macroeconomics Annual, University of Chicago Press, vol. 27(1), pages 375-419.
    2. 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.
    3. 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.
    4. Ming Shann Tsai & Shu Ling Chiang, 2016. "The Valuation Model for a Risky Asset When Its Risky Factors Follow Gamma Distributions," International Review of Finance, International Review of Finance Ltd., vol. 16(3), pages 421-444, September.
    5. Santiago Carbó-Valverde & Sergio Mayordomo & Francisco Rodríguez-Fernández, 2018. "Disentangling the Effects of Household Financial Constraints and Risk Profile on Mortgage Rates," The Journal of Real Estate Finance and Economics, Springer, vol. 56(1), pages 76-100, January.
    6. 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.
    7. 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.
    8. Michael C. S. Wong & Ho Ming Ho, 2023. "A Framework for Integrating Extreme Weather Risk, Probability of Default, and Loss Given Default for Residential Mortgage Loans," Sustainability, MDPI, vol. 15(15), pages 1-16, August.

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