ON THE CREDIT RISK OF SECURED LOANS WITH MAXIMUM LOAN-TO-VALUE COVENANTS

Fabian Astic () and Agnès Tourin ()
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Fabian Astic: Moody's Investors Service, Credit Policy/Research, 7 World Trade Center, 250 Greenwich Street, New York, NY 10007, USA
Agnès Tourin: Department of Finance and Risk Engineering, New York University Polytechnic School of Engineering, Six MetroTech Center, Brooklyn, NY 11201, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 08, 1-19

Abstract: We propose a framework for analyzing the credit risk of secured loans with maximum loan-to-value covenants. Here, we do not assume that the collateral can be liquidated as soon as the maximum loan-to-value is breached. Closed-form solutions for the expected loss are obtained for nonrevolving loans. In the revolving case, we introduce a minimization problem with an objective function parameterized by a risk reluctance coefficient, capturing the trade-off between minimizing the expected loss incurred in the event of liquidation and maximizing the interest gain. Using stochastic control techniques, we derive the partial integro-differential equation satisfied by the value function, and solve it numerically with a finite difference scheme. The experimental results and their comparison with a standard loan-to-value-based lending policy suggest that stricter lending decisions would benefit the lender.

Keywords: Secured loans; stochastic control; finite difference method; viscosity solutions (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500551

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