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Optimal ROE loan pricing with or without adverse selection

Author

Listed:
  • B V Oliver

    (Sandia Corporation, Albuquerque, USA)

  • R M Oliver

    (University of California, Berkeley, USA)

Abstract

The authors describe the structural solution of the loan rate as a function of default and response risk that maximizes expected return on equity for a lender's portfolio of risky loans. Under the assumptions of our model, the non-linear differential equation for the optimizing price is found to be separable in transformed financial, response and risk variables. With an end-point condition where default-free borrowers are willing to borrow at loan rates higher than the lender's cost of funds, general solutions are obtained for cases where default probabilities may depend explicitly on the offered loan rate and where adverse selection may or may not be present. For the general solution, we suggest a numerical algorithm that involves the sequential solutions of two separate transcendental equations each one of which depends on parameters of the risk and response scores. For the special case where the borrower's default probability is conditionally independent of loan rate, it is shown that the optimal solution is independent of Basel regulations on equity capital.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:65:y:2014:i:3:p:435-442
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    Citations

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    Cited by:

    1. Christopher Bockel-Rickermann & Sam Verboven & Tim Verdonck & Wouter Verbeke, 2023. "A Causal Perspective on Loan Pricing: Investigating the Impacts of Selection Bias on Identifying Bid-Response Functions," Papers 2309.03730, arXiv.org.
    2. 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.
    3. Jonathan Crook & David Edelman, 2014. "Special issue credit risk modelling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(3), pages 321-322, March.

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