Optimal Loan Interest Rate Contract Design

Posted: 2 Oct 2002

See all articles by Robert H. Edelstein

Robert H. Edelstein

University of California, Berkeley - Fisher Center for Real Estate and Urban Economics

Branko Urosevic

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

Our paper develops a theoretical framework for analyzing optimal loan interest rate contracts under conditions of risky, symmetric information. We obtain a series of closed form solutions for one-period (static) and multi-period (dynamic) optimal contracts. The optimal design for loan interest rate contracts depends upon the volatility of, and co-variation among the market interest rate, borrower collateral, and borrower income, as well as the loan contract time horizon and the risk preferences of lenders and borrowers. Our analysis demonstrates that for a risk averse borrower with stochastic collateral, variable interest rate contracts, if structured properly, are, in general, Pareto optimal. If the collateral value and/or borrower's future income are positively correlated with the market interest rate, optimal loan interest rate contracts will allocate more interest rate risk sharing to the borrower vis-a-vis the lender than would be the case in the absence of such correlation. This result occurs because the positive correlations make it "easier" for the borrower to repay loans when market interest rates rise, and vice versa. This, in turn, would enable the lender to reduce his risk exposure by receiving higher loan interest rate payments as market interest rates rise, and vice versa. The opposite would be true when the correlation between total borrower's wealth and the market interest rates is negative. While the specific optimal loan interest rate contract may be senstivie to the set of assumptions made, for plausible sets of assumptions, the optimal loan interest rate contract for the multi-period (dynamic) model often exhibits "muted" responses to changes in the market interest rate, making fixed rate loan contracts a reasonable approximation for the optimal design. That may explain why, in the absence of optimal contracts, long-term borrowers tend to prefer fixed rate contracts, while short-term borrowers tend to prefer variable rates contracts. These conclusions are reinforced when exogenous prepayments and defaults are incorporated into our analysis.

Keywords: Optimal loan contract, adjustable rate mortgage, interest rate loan contract, intertemporal loan contracts

Suggested Citation

Edelstein, Robert H. and Urosevic, Branko, Optimal Loan Interest Rate Contract Design. Available at SSRN: https://ssrn.com/abstract=319882

Robert H. Edelstein (Contact Author)

University of California, Berkeley - Fisher Center for Real Estate and Urban Economics ( email )

Haas School of Business
Berkeley, CA 94720-1900
United States
510-643-6105 (Phone)
510-643-7357 (Fax)

Branko Urosevic

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
34-93-542-2590 (Phone)

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