Optimal Stopping and Losses on Subprime Mortgages
DENNIS R. CAPOZZA
University of Michigan Business School, Ann Arbor, MI 48109-1234, USA
THOMAS A. THOMSON
University of Texas, San Antonio, TX 78249-0633, USA
Lender losses on mortgage loans arise from a two-stage process. In the first stage, the borrower stops making
payments if and when default is optimal. The second stage is a lengthy and costly period during which the
lender employs legal remedies to obtain possession and execute a sale of the collateral. This research uses data
on subprime mortgage losses to explore the role of borrower and collateral characteristics, and local legal
requirements, as well as traditional option variables in the decisions of borrowers and lenders. Although
subprime borrowers default earlier, which should reduce lender losses, these borrowers, nevertheless, impose
greater realized losses on mortgage lenders.
Key Words: subprime, mortgages, defaults, losses, lending
In option pricing models of borrower behavior, the decision to default is an optimal
stopping problem. At the optimal time of default, the borrower is balancing the value of
the flow of services from the property (the Bimputed^ rent) versus the size of the
mortgage payment and the value of the collateral against the principle balance of the
mortgage. If the loan is a recourse loan so that the borrower can be pursued for any
deficiency on sale, then borrower assets, income, and credit rating will also play a role in
the decision to default.
Clearly, the decision to default is complex and one where the richness of the decision
will not be captured in simple option pricing models. Nevertheless, numerous insights
arise from viewing the decision from the option pricing perspective.
At what price has the value of the house fallen low enough, so that one’s optimal
action is to default? Option pricing shows that the house price must be lower than the
balance on the loan, and depends on interest rates and transactions costs, not just the
value of the home relative to the mortgage.
Because interest rates are determined in
national markets, their effect should be similar among borrowers. Transactions costs,
however, are more heterogeneous. Relevant considerations include state law and various
personal factors including the so-called Btrigger events.^
The Journal of Real Estate Finance and Economics, 30:2, 115–131, 2005
2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.