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

• 成果类型: Article
• 署名作者: Chun, So Yeon; Lejeune, Miguel A.
• 署名单位: Georgetown University; INSEAD Business School; George Washington University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2019.3378
• 发表日期: 2020
• 页码: 3735-3753
• 关键词: Pricing; revenue management; Credit risk; marginal risk; Value at risk; conditional value at risk; Willingness to pay; mixed-integer nonlinear stochastic programming

摘要

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 non-linear 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.