The recent housing market crisis has brought attention to the so&called subprime mortgage market, which ex& perienced exponential growth over the past few years. The share of subprime mortgages to total originations increased from 6% in 2002 to 20% in 2006. As of 2006, the value of U.S. subprime mortgages was estimated at $1.5 trillion, or 15% of the $10 trillion residential mortgage market.1 Subprime mortgages account for a significant part of the recent increase in household mortgage debt in the United States, from about 60% of GDP in 2003 to above 75% of GDP in 2006.2 It is widely believed that subprime lending has played a major role in the housing market meltdown in 2007.
Unlike traditional prime mortgages, subprime mortgages are normally made out to higher&risk borrowers who buy pricey houses relative to their income level and make little or no downpayment. Often, these mortgages come with incentives including low initial teaser rates, which later reset to higher rates. As a result, subprime mortgage loans have a much higher rate of default than prime mortgage loans.
Because of high default rates among subprime borrowers and big losses among subprime investors, sub& prime mortgages have caused a storm of controversy and criticism. Some critics accuse subprime lenders of predatory lending to naive borrowers who do not fully understand mortgage terms. Others say that subprime underwriters issued mortgages to people who could not afford to pay them back, and then quickly sold their mortgages to outside investors in the form of mortgage&backed securities. Most critics agree that subprime loans do not make sense and should have not been made in the first place. On the other hand, other experts argue that the fast growth of the subprime market was caused by the fast home price appreciation observed in the beginning of the 21st century.
To better understand the nature of the subprime crisis, it is important to examine what caused the rapid growth of the subprime market before the crisis started. This paper seeks to determine whether subprime lending can be explained by rational behavior of BOTH borrowers and lenders. In particular, can stochastic house appreciation, i.e., housing boom followed by housing slump, explain the fast growth of the subprime market during the boom and its meltdown during the slump if both lenders and borrowers have rational expectations about the future states of the housing market?
To address this question, we consider a dynamic continuous time model with a risky borrower, stochastic home appreciation, costly liquidation and a moral hazard problem. We adopt a two&step approach. First, assuming full rationality, we derive an optimal mortgage contract, i.e., the best possible incentive&compatible contract between the borrower and the lender, as a solution to a general dynamic contracting problem. Then we examine whether features of existing mortgage contracts are consistent with the properties of the optimal contract.
Specifically, we consider a continuous&time setting in which a borrower with limited liability needs outside financial support from a risk&neutral lender in order to purchase a house. Home ownership generates for the borrower a public and deterministic utility stream. The borrowerks consumption is divided into two categories: VnecessaryV consumption, which includes grocery food, medicine, transportation and other goods and services essential for the household survival, and VluxuryV consumption, which includes everything else. We assume that the borrower is infinitely risk averse with respect to necessary consumption and risk neutral with respect to luxury consumption. The minimum level of necessary consumption is given by an exogenous stochastic process. After paying for his necessary consumption, the borrower is free to allocate the remaining part of his income among luxury consumption, saving and debt repayment. The distribution of the VexcessV income, which the borrower can use to pay back his debt, is publicly known, however its realizations are privately observable by the borrower.
We assume that the housing market at time zero is in the boom phase, during which the home appreciates at a constant rate. However, at any time the boom can turn into the slump with a certain probability, in which case the home loses its value and the housing market becomes illiquid. The price process is exogenous, and the borrower and the lender have rational expectations. We assume that the borrower and the lender are suffi ciently small so that their actions have no effect on macroeconomic variables such as the market price of the home.
Before the purchase of the house, the borrower and the lender sign a contract that will govern their rela& tionship in the future. The contract specifies transfers between the borrower and the lender, conditional on the history of the borrowerks income reports and the state of the housing market, as well as the circumstances under which the lender would foreclose the loan and seize the home. The borrower has limited liability and can default on the mortgage contract at any time. The borrower has also the option to sell the home. We assume that selling the home in the boom phase is more effi cient than liquidating it through the repossession process due to associated dead&weight costs.
We characterize the optimal allocation using three state variables: the state of the housing market (i.e., the boom or slump), the market home price, and the borrowerks continuation utility (i.e., the expected payoff to the borrower provided he acts optimally given the terms of his contract with the lender). We find that it is optimal to subsidize subprime borrowers, i.e., the borrowers with low continuation utility, during the boom. Default clustering among subprime borrowers is optimal during the slump. It is optimal to insure prime borrowers, i.e., the borrowers with high continuation utility, against the slump.
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Stochastic House Appreciation and Optimal Subprime Lending
