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A Real Option Approach to the Valuation of the Default Risk of Residential Mortgages

Author

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  • Angela C. De Luna López

    (Ernst and Young Madrid, Calle de Raimundo Fernández Villaverde, 65, 28003 Madrid, Spain)

  • Prosper Lamothe-López

    (Department of Financial Economics and Accounting, Universidad Rey Juan Carlos, 28933 Madrid, Spain)

  • Walter L. De Luna Butz

    (Ibero Capital Management, 28006 Madrid, Spain)

  • Prosper Lamothe-Fernández

    (Department of Finance, Universidad Autónoma de Madrid (UAM), 28049 Madrid, Spain)

Abstract

A significant share of many commercial banks’ portfolios consists of residential mortgage loans provided to individuals and families. This paper examines the default and rational prepayment risk of single-borrower (residential) mortgage loans based on an option pricing model that captures the skewness and kurtosis of the house prices returns’ distribution via the shifted lognormal distribution. Equilibrium option-adjusted credit spreads are obtained from the implementation of the model under plausible values of the relevant parameters. The methodology involves numerical experiments, using a shifted binomial tree model by Haathela and Camara and Chung, to evaluate the effects of the loan-to-value (LTV) ratio, asset volatility, interest rates, and recovery costs on mortgage valuation. Findings indicate prepayment risk significantly influences loan value, as it limits upside potential, while LTV and volatility directly impact default risk. The shifting parameter (θ) in the asset distribution proves essential for accurate risk assessment. Conclusions emphasize the need for mortgage underwriting to consider specific asset characteristics, optimal loan structures, and prevailing risk-free rates to avoid underestimating risk. This model can aid in the more robust pricing and management of mortgage portfolios, especially relevant in regions with substantial mortgage-backed exposure, such as the European banking system.

Suggested Citation

  • Angela C. De Luna López & Prosper Lamothe-López & Walter L. De Luna Butz & Prosper Lamothe-Fernández, 2025. "A Real Option Approach to the Valuation of the Default Risk of Residential Mortgages," IJFS, MDPI, vol. 13(1), pages 1-25, March.
    • Handle: RePEc:gam:jijfss:v:13:y:2025:i:1:p:31-:d:1603206
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    References listed on IDEAS

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    1. James F. Epperson & James B. Kau & Donald C. Keenan & Walter J. Muller, 1985. "Pricing Default Risk in Mortgages," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 13(3), pages 261-272, September.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Dennis R. Capozza & Dick Kazarian & Thomas A. Thomson, 1998. "The Conditional Probability of Mortgage Default," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 26(3), pages 259-289, September.
    5. Xudong An & Yongheng Deng & Stuart A Gabriel, 2021. "Default Option Exercise over the Financial Crisis and beyond [Predatory lending and the subprime crisis]," Review of Finance, European Finance Association, vol. 25(1), pages 153-187.
    6. António Câmara & San‐Lin Chung, 2006. "Option pricing for the transformed‐binomial class," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(8), pages 759-788, August.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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