Journal of Real Estate Finance and Economics, 24:1/2, 35±58, 2002
# 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.
Mortgage Contracts, Strategic Options and Stochastic
ROBERT A. JONES
Simon Fraser University
Colorado State University and FreddieMac
This paper offers a game-theoretic model for both the analysis and valuation of mortgage contracts in the context
of an economy with complete information and complete contingent claims markets. We analyze the equilibrium
strategy of the lender, who holds an option over the magnitude of mortgage credit extended per dollar of collateral
offered, and the mortgagor, who holds options to default or prepay, in a class of intertemporal mortgage contracts
collateralized by property evolving according to a random process which is common knowledge to both parties to
the mortgage contract. Using continuous±time arbitrage valuation principles, we derive the value of the mortgage
contract to both parties and show, through both analytical solutions and numerical simulations, that Markov
perfect equilibria exist in which, among other properties, a lower ¯ow of housing services accruing to the
borrower, per dollar of initial house value, and a correspondingly lower rate of effective depreciation, will elicit a
larger volume of funds offered by a lender; the amount of credit offered, the values of the contract to both lender
and mortgagor, and the expected losses to both parties from costly bankruptcy are highly sensitive to the
perceived volatility of the value of the property collateralizing the mortgage, even in an economy with complete
markets or risk neutrality on the parts of lender and borrower; the upper limit on mortgage credit offered by a
rational lender may be a small fraction of the current fair market value of the property, regardless of the
contractual yield offered by the borrower, and will decrease, at each such yield, as bankruptcy costs or housing
service ¯ows increase; and under signi®cant but plausible values for bankruptcy and costs of liquidating property
under foreclosure, the ¯ow of mortgage credit can become negatively related to the spread of the mortgage yield
over the riskless rate, with the lender preferring a lower contractual yield to a higher one.
Key Words: regulated Brownian motion, real options, differential games
The nature of mortgage lending and the ef®ciency of residential mortgage markets are
important topics in ®nancial economics and in public policy. Aprerequisite for assessing
the state of the mortgage market is the ability to model the strategic behavior of both the
lender and borrower and to value the claims of each party in the mortgage contract which
emerges in the resulting equilibrium.
Author for correspondence: Professor David Nickerson, Department of Economics, Colorado State University,
Clark Hall C310, Fort Collins, Colorado 80523-1771, USA.