On the Credit Risk of Secured Loans with Maximum Loan-to-Value Covenants

We propose a framework for analyzing the credit risk of secured loans under historical probability. We assume that the collateral cannot be liquidated immediately. Closed-form solutions for the expected loss are obtained for non-revolving loans. In the revolving case, we introduce a minimization problem with a loss function parameterized by a risk reluctance coefficient. We use stochastic control techniques to derive the Partial Integro-Differential Equation satisfied by the value function, and solve it numerically with a finite difference scheme. We exhibit optimal strategies and compare them with the standard LTV-based lending policy