Credit card pricing and impact of adverse selection

Variable pricing is one way of improving the profitability of credit cards when the price is the interest rate to be charged. However, choosing the appropriate price for each risk grade of default is not straightforward, as one of the main problems is adverse selection, when the lender finds that the borrowers who actually take a specific offer have a higher default rate than expected. We show that modelling the choice of credit card by the borrower as an auction process means that the winner's curse can lead to adverse selection. By modelling the way lenders use the credit score of a borrower in their pricing decision we are able to show that there is a simple relationship between the actual probability of a borrower repaying and what the successful lender believes this probability to be, regardless of the distribution of the errors caused by adverse selection. This allows one to assess the impact on profitability of these errors.