COLLATERAL EQUILIBRIUM: A BASIC FRAMEWORK

Journal of Mathematical Finance, 2015

The author examines the role of collateral in an environment where lenders and borrowers possess identical information and similar beliefs about its future value. Using option-pricing techniques, he shows that a secured loan contract is equivalent to a regular bond and an embedded option to the borrower to default. The author finds that the lender will not advance to the borrower, a loan that exceeds the market value of the collateral, and that the supply of loans increases with a rise in the market value of the collateral. Increases in the volatility of the value of the collateral, interest rate, and dividend rate of the collateral independently depress the loan supply. The author also derives the cost of a third-party guarantee of a loan and an implied risk premium.

2003

The author examines the role of collateral in an environment where lenders and borrowers possess identical information and similar beliefs about its future value. Using option-pricing techniques, he shows that a secured loan contract is equivalent to a regular bond and an embedded option to the borrower to default. He finds that the lender will not advance to the borrower a loan that exceeds the market value of the collateral, and that the supply of loans increases with a rise in the market value of the collateral. Increases in the volatility of the value of the collateral, interest rate, and dividend rate of the collateral independently depress the loan supply. The author also derives the cost of a third-party guarantee of a loan and an implied risk premium.

2005

Abstract To explain the variation in US asset returns in the 20th century, we solve an equilibrium model in which households face housing collateral constraints. An increase in the ratio of housing to human wealth loosens these constraints. It allows for more risk sharing and decreases the rate of return that households require for holding equity. This collateral mechanism can explain the time-variation in equity and risk-free debt returns and the cross-sectional variation in equity returns in the US.

SSRN Electronic Journal, 2000

In this paper we examine the effect of collateral requirements on the prices of longlived assets. We consider a Lucas-style infinite-horizon exchange economy with heterogeneous agents and collateral constraints. There are two trees in the economy which can be used as collateral for short-term loans. For the first tree the collateral requirement is determined endogenously while the collateral requirement for loans on the second tree is exogenously regulated. We show that the presence of collateral constraints and the endogenous margin requirements for the first tree lead to large excess price-volatility of the second tree. Changes in the regulated margin requirements for the second tree have large effects on the volatility of both trees. While tightening margins for loans on the second tree always decreases the price volatility of the first tree, price volatility of the second tree might very well increase with this change. In our calibration we allow for the possibility of disaster states. This leads to very large quantitative effects of collateral requirements and to realistic equity risk premia. We show that our qualitative results are robust to the actual parametrization of the economy.

The Journal of Real Estate Finance and Economics, 2011

This paper presents a systematic framework for capturing the collateraldriven mortgage default risk. A forward-looking home price distribution model is developed that explicitly incorporates different sources of volatility in the market value of collateral houses. A consistent and computationally-efficient top-down approach of home price simulation is also introduced. We show that with the proper inclusion of all relevant sources of volatilities, the top-down approach provides close approximation to the results generated by a theoretically sound but computationally demanding bottom-up simulation approach. Using a numerical simulation, we demonstrate that a geographically-diversified mortgage pool entails a substantially lower level of systematic collateral driven mortgage default risk compared to a spatially-concentrated pool. However, the expected default risk is shown to remain unaffected, indicating that the benefit from geographic diversification is only realized through lower risk-based capital requirements, not in lower mortgage insurance premiums. Based on the US state level house price indices, the systematic risk of a state-concentrated mortgage pool is estimated to be about four times higher than that of a nationally-diversified mortgage pool. Our results also show that, among the different volatility components, omitting the cross-sectional dispersion of

SSRN Electronic Journal, 2000

Financially constrained borrowers have the incentive to influence the appraisal process in order to increase borrowing or reduce the interest rate. We document that the average valuation bias for residential refinance transactions is above 5%. The bias is larger for highly leveraged transactions, around critical leverage thresholds, and for transactions mediated through a broker. Mortgages with inflated valuations default more often; however, lenders partly account for the valuation bias through pricing. Sumit Agarwal Associate Professor of Finance and Real Estate NUS Business School Mochtar Raidy Building, BIZ1 15 Kent Ridge Road

Journal of Economic Surveys, 2000

This paper surveys existing explanations for the pervasive use of collateral in credit markets and relates them to the empirical evidence on the subject. Collateral may be used as a screening or an incentive device in markets characterized by various forms of asymmetric and biased information. The evidence is incompatible with the use of collateral as a signal of projects' quality, while broadly consistent with explanations based on its incentive properties and asymmetric evaluation of projects.

SSRN Electronic Journal, 2017

We examine the role of collateral in a dynamic model of optimal credit contracts in which a borrower values both housing and non-housing consumption. The borrower's private information about his income is the only friction. An optimal contract is collateralized when in some state, some portion of the borrower's net worth is forfeited to the lender. We show that optimal contracts are always collateralized. The total value of forfeited assets is decreasing in income, highlighting the role collateral as a deterrent to manipulation. Some assets, those that generate consumable services will necessarily be collateralized while others may not be. Endogenous default arises when the borrower's initial wealth is low, as with subprime borrowers, and/or his future earnings are highly variable.

2000

Abstract Personal bankruptcy makes financial contracts hard to enforce puts because it weakens the punishment technologies available to creditors. I consider a generic endowment economy in which agents trade a complete set of contingent claims. As in Alvarez and Jermann (2000), these contracts are not enforceable. In this model, when households default, they cannot be excluded from financial markets but they lose all of the collateral.

Journal of Economic Theory, 2008

This paper presents a microfounded model of money where durable assets serve as a guarantee to repay consumption loans. We study a steady state equilibrium where money and credit coexist. In such an equilibrium, a larger investment in durable capital relaxes the borrowing constraint faced by consumers. We show that the occurrence of over-investment and the behavior of capital accumulation depend on the rate of inflation, the relative risk aversion of agents and the marginal productivity of the capital goods. is a [0, 1] continuum of infinitely-lived agents. Each period is divided into two sub-periods, called day and night. A perfectly competitive market opens in each sub-period. Economic activity differs between day and night. During the day, agents can trade a perishable consumption good and face randomness in their preferences and production possibilities. An agent is a buyer with probability σ in which case he wants to consume but cannot produce, whereas an agent is a seller with probability 1 − σ in which case he is able to produce but does not wish to consume. 4 During the night, agents can trade a durable good that can be used for consumption or investment. In contrast to the first sub-period, there is no randomness in the second sub-period, and all agents can produce and consume simultaneously.