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A New Look on the Profitability of Fixed and Indexed Mortgage Products

Author

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  • Paoyu Huang

    (Department of International Business, Soochow University, Taipei 100006, Taiwan)

  • Chih-Te Yang

    (Department of Business Administration, Tamkang University, New Taipei City 251301, Taiwan)

  • Yuhsin Chen

    (Department of Accounting, Chung Yuan Christian University, Taoyuan 320314, Taiwan)

  • Yensen Ni

    (Department of Management Sciences, Tamkang University, New Taipei City 251301, Taiwan)

Abstract

This study presents a novel approach to analyzing the present value of total profit for fixed and indexed mortgage products in order to determine the optimal mortgage interest rate that would maximize the bank’s expected total profit based on applying the approach used in operations research to the field of finance. The study considers the impact of lending rate, demand, prepayment, and defaults on bank profits and emphasizes the trade-offs between potential gains and losses when setting the lending rate. As such, we not only used a fixed-rate mortgage model or an index mortgage model with the interest rate as the decision variable, but also employed mathematical analysis methods to find out the loan rate that maximizes the present value of the bank’s expected total profit. The findings revealed that an increase in interest rate, loan amount, and demand positively impacted the bank profits, while prepayment had an adverse effect. The study highlights the importance of carefully evaluating various factors that influence revenue in order to arrive at the most appropriate lending rate that will optimize profits. The results provide valuable insights into the optimal mortgage interest rate and the factors that determine the revenue and profits of a bank, with implications for cost–benefit analysis, fixed-rate mortgage, indexed mortgage, lending rate, defaults, and maximum profit. This study contributes to the existing literature on mortgage products. It provides practical implications for banks in managing their mortgage products efficiently in order to enhance their financial performance and recommends optimizing mortgage interest rates for maximum bank profits by taking the lending rate, demand, and prepayment effects into account.

Suggested Citation

  • Paoyu Huang & Chih-Te Yang & Yuhsin Chen & Yensen Ni, 2023. "A New Look on the Profitability of Fixed and Indexed Mortgage Products," Mathematics, MDPI, vol. 11(17), pages 1-16, August.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3631-:d:1222785
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    References listed on IDEAS

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    1. Wai K. Leung & C. F. Sirmans, 1990. "A Lattice Approach to Pricing Fixed‐Rate Mortgages with Default and Prepayment Options," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 18(1), pages 91-104, March.
    2. Mester, Loretta J. & Saunders, Anthony, 1995. "When does the prime rate change?," Journal of Banking & Finance, Elsevier, vol. 19(5), pages 743-764, August.
    3. Aytek Malkhozov & Philippe Mueller & Andrea Vedolin & Gyuri Venter, 2016. "Mortgage Risk and the Yield Curve," The Review of Financial Studies, Society for Financial Studies, vol. 29(5), pages 1220-1253.
    4. Ying Jiao & Shanqiu Li, 2018. "Modeling Sovereign Risks: From A Hybrid Model To The Generalized Density Approach," Mathematical Finance, Wiley Blackwell, vol. 28(1), pages 240-267, January.
    5. Igor Livshits & James C. Mac Gee & Michèle Tertilt, 2016. "The Democratization of Credit and the Rise in Consumer Bankruptcies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(4), pages 1673-1710.
    6. Meng-Jou Lu & Cathy Yi-Hsuan Chen & Wolfgang Karl Hardle, 2020. "Copula-Based Factor Model for Credit Risk Analysis," Papers 2009.12092, arXiv.org, revised Oct 2020.
    7. 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.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    9. Peter Bank & Ibrahim Ekren & Johannes Muhle-Karbe, 2018. "Liquidity in Competitive Dealer Markets," Papers 1807.08278, arXiv.org, revised Mar 2021.
    10. Peter Bank & Ibrahim Ekren & Johannes Muhle‐Karbe, 2021. "Liquidity in competitive dealer markets," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 827-856, July.
    11. Molyneux, Philip & Reghezza, Alessio & Xie, Ru, 2019. "Bank margins and profits in a world of negative rates," Journal of Banking & Finance, Elsevier, vol. 107(C), pages 1-1.
    12. Fredrik Åkesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.
    13. Srinivasan, Venkat & Kim, Yong H, 1987. "Credit Granting: A Comparative Analysis of Classification Procedures," Journal of Finance, American Finance Association, vol. 42(3), pages 665-681, July.
    14. Cheng-Hong Yang & Borcy Lee & Yu-Da Lin, 2022. "Effect of Money Supply, Population, and Rent on Real Estate: A Clustering Analysis in Taiwan," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    15. Forbes, Shawn M. & Mayne, Lucille S., 1989. "A friction model of the prime," Journal of Banking & Finance, Elsevier, vol. 13(1), pages 127-135, March.
    16. Corsaro, Stefania & De Simone, Valentina & Marino, Zelda, 2021. "Split Bregman iteration for multi-period mean variance portfolio optimization," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    17. Brent W. Ambrose & Michael LaCour‐Little, 2001. "Prepayment Risk in Adjustable Rate Mortgages Subject to Initial Year Discounts: Some New Evidence," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 29(2), pages 305-327.
    18. Fabien Guilbaud & Huyên Pham, 2015. "Optimal High-Frequency Trading In A Pro Rata Microstructure With Predictive Information," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 545-575, July.
    19. Antonio Díaz & Marta Tolentino, 2020. "Risk Management for Bonds with Embedded Options," Mathematics, MDPI, vol. 8(5), pages 1-12, May.
    20. Stefania Corsaro & Valentina De Simone & Zelda Marino & Salvatore Scognamiglio, 2022. "l 1 -Regularization in Portfolio Selection with Machine Learning," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
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