Default, Credit Scoring, and Loan-to-Value: A Theoretical Analysis Under Competitive and Non-Competitive Mortgage Markets

Abstract

Consistent with existing literature, we first show that when borrowers' default probability on the mortgage loan is unobservable to the lender, the latter can screen borrowers by their combined choice of loan-to-value (LTV) ratio and interest rate. We further demonstrate that when borrowers also signal their default risk by acquiring a credit score, then a combined separating signaling and screening equilibrium is attained. If the signaling cost is sufficiently small, the combined signaling and screening equilibrium dominates the screening only equilibrium under both competitive and non-competitive market frameworks. However, while, under the competitive setting, borrowers benefit from constituting a credit scoring signaling system, the prospective gain is shifted to lenders under collusion. Finally, we show that under both competitive and non-competitive combined signaling and screening equilibria, high and low risk borrowers, while acquiring distinct credit scores (and therefore paying different interest rates) might realize higher, lower, or identical LTV ratios. Hence, any empirical test of the relation between LTV ratio and default risk must incorporate the interrelation among the LTV ratio, credit score, and interest rate.