Credit price optimisation within retail banking

Abstract

The willingness of a customer to pay for a product or service is mathematically captured by a price elasticity model. The model relates the responsiveness of customers to a change in the quoted price. In addition to overall price sensitivity, adverse selection could be observed whereby certain customer segments react dierently towards price changes. In this paper the problem of determining optimal prices to quote prospective customers in credit retail is addressed such that the interest income to the lender will be maximised while taking price sensitivity and adverse selection into account. For this purpose a response model is suggested that overcomes non-concavity and unrealistic asymptotic behaviour which allows for a linearisation approach of the non-linear price optimisation problem. A two-stage linear stochastic programming formulation is suggested for the optimisation of prices while taking uncertainty in future price sensitivity into account. Empirical results are based on real data from a nancial institution.

Key words: Pricing, banking, optimization, stochastic programming.