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Pricing and revenue management for bank home loans: a mathematical approach

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Abstract

In this study, we formulate both dynamic and static pricing models for home loans for a bank. These models optimize the net present value of money available at the end of 15 years, subject to pricing limits and cash flows. We collected actual data from a leading nationalized bank in India to develop a relationship between interest rate (price) and number of loans sanctioned (demand). We then assume different versions of the demand function (linear, exponential and rectangular hyperbola). We also develop the relationship of default probability as a function of interest rate. For the three demand functions, we evaluate the expected revenue at the end of the nth period for both static and dynamic pricing models for home loans and compare the results. We also discuss the sensitivity of the study result to changes in the parameters of the demand equations for dynamic pricing model.

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Availability of data and materials

The raw data that support the findings of this study are available from a leading nationalized bank from one of the states in India. After discussing with the bank officials, data cleaning was performed on the raw data received from the bank and the cleaned data that was used for this study is provided in the manuscript. The restrictions do apply to the availability of raw data, which were used for the current study, and so are not publicly available. The data is however available from the authors upon reasonable request.

References

  1. Beck, T., Ioannidou, V., Schäfer, L.: Foreigners vs. natives: Bank lending technologies and loan pricing. Management Science. 64(8), 3792–820 (2017)

    Article  Google Scholar 

  2. Chakravarty, S., Scott, J.: Relationships and Rationing in Consumer Loans. J. Business 72(4), 523–544 (1999)

    Article  Google Scholar 

  3. Duca, J.V., Rosenthal, S.S.: An empirical test of credit rationing in the mortgage market. J. Urban Econ. 29(2), 218–234 (1991)

    Article  Google Scholar 

  4. Finn, W.T., II., Frederick, J.B.: Managing the margin. Am. Bank. Assoc. ABA Bank. J. 84(4), 50 (1992)

    Google Scholar 

  5. Fourer, R., Gay, D.M., Kernighan, B.W.: A modelling language for mathematical programming. Manage. Sci. 36(5), 519–554 (1990)

    Article  Google Scholar 

  6. Hannagan, T.A.: 8,000 institutions can be wrong: loan pricing in the 21st Century. RMA J. 85(1), 60–65 (2002)

    Google Scholar 

  7. Hoskins, W.G.: How to price loans to increase profits. Am. Bank. Assoc. ABA Bank. J. 80(10), 12 (1988)

    Google Scholar 

  8. Hoskins, W.G.: Keeping loan pricing rational and profitable. ABA Bank. J. 82(12), 15 (1990)

    Google Scholar 

  9. Kent, R.: Credit rationing and the home mortgage market. J. Money, Credit, Bank. 12(3), 488–501 (1980)

    Article  Google Scholar 

  10. Khedlekar, U.K., Shukla, D.: Dynamic pricing model with logarithmic demand. Opsearch 50(1), 1–13 (2013)

    Article  Google Scholar 

  11. Maldonado, S., Peters, G., Weber, R.: Credit scoring using three-way decisions with probabilistic rough sets. Information Sciences. 507, 700–14 (2018)

    Article  Google Scholar 

  12. Marks, P.C.: Improving the earnings engine [2]. Am. Bank. Association. ABA Bank. J. 79(8), 48 (1987)

    Google Scholar 

  13. Ng, C.T., Ding, Q., Cheng, T.C.E., Lam, S.S.: Preemptive repayment policy for multiple loans. Ann. Oper. Res. 192(1), 141–150 (2012)

    Article  Google Scholar 

  14. Owens, J., Sibbald, E., Harndon, A.: Hot to improve net interest margins. ABA Bank. J. 83(3), 56 (1991)

    Google Scholar 

  15. Phillips, R.L., Raffard, R.: Price-Driven Adverse Selection in Consumer Lending. Columbia University, USA (2011)

    Google Scholar 

  16. Phillips, R.L., Rhode, F.: “Loan Pricing”, Pricing and revenue optimization. RMA J. 2006, 80–83 (2006)

    Google Scholar 

  17. Phillips, R.L.: “Customized Pricing”. Chapter 11 Pricing and revenue optimization. Stanford University Press, USA (2005)

    Book  Google Scholar 

  18. Rosenthal, S., Duca, J., Gabriel, S.: Credit rationing and the demand for owner-occupied housing. J. Urban Econ. 29, 48–63 (1991)

    Article  Google Scholar 

  19. Rubin, G.M., Overstreet, G.A., Beling, P., Rajaratnam, K.: A dynamic theory of the credit union. Ann. Oper. Res. 205(1), 29–53 (2013)

    Article  Google Scholar 

  20. Seshadri, S., Khanna, A., Harche, F., Wyle, R.: A method for strategic asset-liability management with an application to the Federal Home Loan Bank of New York. Oper. Res. 47(3), 345–360 (1999)

    Article  Google Scholar 

  21. Thomas, L.C., Oliver, R.W., Hand, D.J.: A survey of the issues in consumer credit modelling research. J. Oper. Res. Soci. 56(9), 1006–1015 (2005)

    Article  Google Scholar 

  22. Thomas, L.C.: Consumer finance: challenges for operational research. J. Oper. Res. Soci. 61(1), 41–52 (2010)

    Article  Google Scholar 

  23. Tobie, J., Houthakker, H.: The effects of rationing on demand elasticities. Rev. Econ. Stud. 18(3), 140–153 (1950)

    Article  Google Scholar 

  24. Ulrich, T.A.: The Financial-Planning Implications of Bank Loan Pricing. J. Account. 150(3), 64 (1980)

    Google Scholar 

Download references

Acknowledgements

We thank the bank for sharing data for this research study. We also thank Ms. Deepali Joshi for proof reading and editing the manuscript.

Funding

This research work is funded by Research and Publications Committee of Indian Institute of Management (IIMA) in 2013–15. An initial version of this paper is available as a working paper on IIMA website as a norm of IIMA. The article submitted to this journal has a similarity index of only 5–6% with that of the working paper on IIMA website. The originality report is attached as a supplementary material.

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Authors and Affiliations

  1. Indian Institute of Management, Vastrapur, Ahmedabad, 380015, India

    Sumeetha Natesan

  2. McKinsey & Company, 605W 42nd Street, Apt 38B, New York, NY, 10036, USA

    Deepika Thakur

  3. Department of Production and Quantitative Methods, Indian Institute of Management, Vastrapur, Ahmedabad, 380015, India

    Goutam Dutta

  4. Director NITIE, National Institute of Industrial Engineering, Vihar Lake, Near‘The Residence Hotel’, Powai, Mumbai, 400087, India

    Manoj Kumar Tiwari

Authors
  1. Sumeetha Natesan
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  2. Deepika Thakur
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  3. Goutam Dutta
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  4. Manoj Kumar Tiwari
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Contributions

SN has majorly contributed in this work by collecting data, developing the optimization model, analysing the model with data, interpreting the results and also drafting the final manuscript; DT has contributed in writing the introduction, literature survey and the initial part of the study in the manuscript; GD contributes to the conception and design of the multi-period optimization model; MKT contributed by modifying the manuscript for formal submission to the OPSEARCH journal. All authors read and approved the final manuscript.

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Correspondence to Goutam Dutta.

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Natesan, S., Thakur, D., Dutta, G. et al. Pricing and revenue management for bank home loans: a mathematical approach. OPSEARCH 60, 656–687 (2023). https://doi.org/10.1007/s12597-023-00624-5

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