IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v66y2020i8p3735-3753.html
   My bibliography  Save this article

Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution

Author

Listed:
  • So Yeon Chun

    () (McDonough School of Business, Georgetown University, Washington, District of Columbia 20057; INSEAD, 77305 Fontainebleau, France)

  • Miguel A. Lejeune

    () (Department of Decision Sciences, George Washington University, Washington, District of Columbia 20052)

Abstract

We consider a lender (bank) that determines the optimal loan price (interest rate) to offer to prospective borrowers under uncertain borrower response and default risk. A borrower may or may not accept the loan at the price offered, and both the principal loaned and the interest income become uncertain because of the risk of default. We present a risk-based loan pricing optimization framework that explicitly takes into account the marginal risk contribution, the portfolio risk, and a borrower’s acceptance probability. Marginal risk assesses the incremental risk contribution of a prospective loan to the bank’s overall portfolio risk by capturing the dependencies between the prospective loan and the existing portfolio and is evaluated with respect to the value-at-risk and conditional value-at-risk measures. We examine the properties and computational challenges of the formulations. We design a reformulation method based on the concavifiability concept to transform the nonlinear objective functions and to derive equivalent mixed-integer nonlinear reformulations with convex continuous relaxations. We also extend the approach to multiloan pricing problems, which feature explicit loan selection decisions in addition to pricing decisions. We derive formulations with multiple loans that take the form of mixed-integer nonlinear problems with nonconvex continuous relaxations and develop a computationally efficient algorithmic method. We provide numerical evidence demonstrating the value of the proposed framework, test the computational tractability, and discuss managerial implications.

Suggested Citation

  • So Yeon Chun & Miguel A. Lejeune, 2020. "Risk-Based Loan Pricing: Portfolio Optimization Approach with Marginal Risk Contribution," Management Science, INFORMS, vol. 66(8), pages 3735-3753, August.
  • Handle: RePEc:inm:ormnsc:v:66:y:2020:i:8:p:3735-3753
    DOI: 10.1287/mnsc.2019.3378
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/mnsc.2019.3378
    Download Restriction: no

    References listed on IDEAS

    as
    1. David B. Gross & Nicholas S. Souleles, 2002. "Do Liquidity Constraints and Interest Rates Matter for Consumer Behavior? Evidence from Credit Card Data," The Quarterly Journal of Economics, Oxford University Press, vol. 117(1), pages 149-185.
    2. Bruche, Max & González-Aguado, Carlos, 2010. "Recovery rates, default probabilities, and the credit cycle," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 754-764, April.
    3. B V Oliver & R M Oliver, 2014. "Optimal ROE loan pricing with or without adverse selection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 435-442, March.
    4. Miguel A. Lejeune & Gülay Samatlı-Paç, 2013. "Construction of Risk-Averse Enhanced Index Funds," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 701-719, November.
    5. Musto, David K. & Souleles, Nicholas S., 2006. "A portfolio view of consumer credit," Journal of Monetary Economics, Elsevier, vol. 53(1), pages 59-84, January.
    6. Dirk Tasche, 2009. "Capital allocation for credit portfolios with kernel estimators," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 581-595.
    7. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    8. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    9. Abdul Abiad & Enrica Detragiache & Thierry Tressel, 2010. "A New Database of Financial Reforms," IMF Staff Papers, Palgrave Macmillan, vol. 57(2), pages 281-302, June.
    10. Bo Huang & Lyn C Thomas, 2015. "The impact of Basel Accords on the lender’s profitability under different pricing decisions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1826-1839, November.
    11. Til Schuermann, 2004. "Why were banks better off in the 2001 recession?," Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 10(Jan).
    12. Magri, Silvia & Pico, Raffaella, 2011. "The rise of risk-based pricing of mortgage interest rates in Italy," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1277-1290, May.
    13. Hamilton Emmons & Stephen M. Gilbert, 1998. "Note. The Role of Returns Policies in Pricing and Inventory Decisions for Catalogue Goods," Management Science, INFORMS, vol. 44(2), pages 276-283, February.
    14. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    15. D. Li & X.L. Sun & M.P. Biswal & F. Gao, 2001. "Convexification, Concavification and Monotonization in Global Optimization," Annals of Operations Research, Springer, vol. 105(1), pages 213-226, July.
    16. Yu, Jing-Rung & Chiou, Wan-Jiun Paul & Mu, Da-Ren, 2015. "A linearized value-at-risk model with transaction costs and short selling," European Journal of Operational Research, Elsevier, vol. 247(3), pages 872-878.
    17. Kimber, Andrew, 2003. "Credit Risk: From Transaction to Portfolio Management," Elsevier Monographs, Elsevier, edition 1, number 9780750656672.
    18. Thomas, Lyn C., 2009. "Consumer Credit Models: Pricing, Profit and Portfolios," OUP Catalogue, Oxford University Press, number 9780199232130.
    19. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2008. "Fast Simulation of Multifactor Portfolio Credit Risk," Operations Research, INFORMS, vol. 56(5), pages 1200-1217, October.
    20. Guangwu Liu, 2015. "Simulating Risk Contributions of Credit Portfolios," Operations Research, INFORMS, vol. 63(1), pages 104-121, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bernd Engelmann & Ha Pham, 2020. "A Raroc Valuation Scheme for Loans and Its Application in Loan Origination," Risks, MDPI, Open Access Journal, vol. 8(2), pages 1-20, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guangwu Liu, 2015. "Simulating Risk Contributions of Credit Portfolios," Operations Research, INFORMS, vol. 63(1), pages 104-121, February.
    2. Dimitris Andriosopoulos & Michalis Doumpos & Panos M. Pardalos & Constantin Zopounidis, 2019. "Computational approaches and data analytics in financial services: A literature review," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(10), pages 1581-1599, October.
    3. M. Dietsch & C. Welter-Nicol, 2014. "Do LTV and DSTI caps make banks more resilient?," Débats économiques et financiers 13, Banque de France.
    4. Dietsch, Michel & Petey, Joël, 2015. "The credit-risk implications of home ownership promotion: The effects of public subsidies and adjustable-rate loans," Journal of Housing Economics, Elsevier, vol. 28(C), pages 103-120.
    5. Leitao, Álvaro & Ortiz-Gracia, Luis, 2020. "Model-free computation of risk contributions in credit portfolios," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    6. Mohamed A. Ayadi & Hatem Ben-Ameur & Nabil Channouf & Quang Khoi Tran, 2019. "NORTA for portfolio credit risk," Annals of Operations Research, Springer, vol. 281(1), pages 99-119, October.
    7. Cheng-Der Fuh & Chuan-Ju Wang, 2017. "Efficient Exponential Tilting for Portfolio Credit Risk," Papers 1711.03744, arXiv.org, revised Apr 2019.
    8. Tang, Qihe & Tang, Zhaofeng & Yang, Yang, 2019. "Sharp asymptotics for large portfolio losses under extreme risks," European Journal of Operational Research, Elsevier, vol. 276(2), pages 710-722.
    9. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    10. Rongda Chen & Ze Wang & Lean Yu, 2017. "Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1101-1124, July.
    11. Cheng, X. & Degryse, H.A., 2010. "Information Sharing and Credit Rationing : Evidence from the Introduction of a Public Credit Registry," Discussion Paper 2010-34S, Tilburg University, Center for Economic Research.
    12. García-Céspedes, Rubén & Moreno, Manuel, 2017. "An approximate multi-period Vasicek credit risk model," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 105-113.
    13. Agarwal, Sumit & Chomsisengphet, Souphala & Liu, Chunlin & Souleles, Nicholas S., 2005. "Do consumers choose the right credit contracts?," CFS Working Paper Series 2005/32, Center for Financial Studies (CFS).
    14. Yan Yuan & Toshiyuki Sueyoshi, 2017. "Effects of balance transfer offers on consumer short-term finance: evidence from credit card data," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 6(1), pages 1-30, December.
    15. Laurent, Jean-Paul & Sestier, Michael & Thomas, Stéphane, 2016. "Trading book and credit risk: How fundamental is the Basel review?," Journal of Banking & Finance, Elsevier, vol. 73(C), pages 211-223.
    16. Hsieh, Ming-Hua & Lee, Yi-Hsi & Shyu, So-De & Chiu, Yu-Fen, 2019. "Estimating multifactor portfolio credit risk: A variance reduction approach," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    17. Malik, Madhur & Thomas, Lyn C., 2012. "Transition matrix models of consumer credit ratings," International Journal of Forecasting, Elsevier, vol. 28(1), pages 261-272.
    18. Avramidis, Panagiotis & Pasiouras, Fotios, 2015. "Calculating systemic risk capital: A factor model approach," Journal of Financial Stability, Elsevier, vol. 16(C), pages 138-150.
    19. Sumit Agarwal & Souphala Chomsisengphet & Chunlin Liu & Nicholas S. Souleles, 2015. "Do Consumers Choose the Right Credit Contracts?," Review of Corporate Finance Studies, Oxford University Press, vol. 4(2), pages 239-257.
    20. Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:66:y:2020:i:8:p:3735-3753. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.