Relocation Opportunities and Mortgage Default

This paper presents a theoretical model of residential mortgage default when borrowers face beneficial as well as costly relocation opportunities. It amplifies and extends previous work by providing explicit conditions leading to default. The model also establishes when a borrower's relocation decision and default decision are dependent and when they are not.
A central result is that there is a range of book equity wherein the decision to default is not determined solely by the current level of equity or the borrower's ability to continue the mortgage payments. Rather, various costs and benefits, both tangible and intangible, enter into the decision. Specific conditions are identified that lead to relocation without default, default and relocation, and no default or relocation. The effects of changes in the variables upon default probability are presented.
Assuming that the borrower does not wish to retain ownership in the property, the model also predicts whether an individual borrower will choose prepayment or default when a relocation is made. The choice depends on the value of the relocation opportunity faced by the borrower, as well as financial variables such as house value, mortgage balance, and transaction costs. This finding suggests that existing empirical analyses of default may have omitted explanatory variables.     

Commercial Mortgage Defaults: Proportional Hazards Estimation Using Individual Loan Histories

This paper examines the theory of commercial mortgage default and tests it using a data set of 2,899 loan histories provided by a major multi-line insurance company. A default model is estimated which relates subsequent default incidence and timing to contemporaneous loan term, borrower, property and economic/market conditions. Maximum likelihood estimation is used to estimate a hazard function predicting conditional probability of default over time. Results confirm many expected default relationships, in particular the dominance of loan terms and property value trends over time in affecting default. The effectiveness of the model in discriminating between "good" and "bad" loans is explored. Implications for underwriting practice and credit risk diversification are noted. Finally, suggestions are made for extending these results in pricing applications.     

Determinants of Multifamily Mortgage Default

Option–based models of mortgage default posit that the central measure of default risk is the loan–to–value (LTV) ratio. We argue, however, that an unrecognized problem with extending the basic option model to existing multifamily and commercial mortgages is that key variables in the option model are endogenous to the loan origination and property sale process. This endogeneity implies, among other things, that no empirical relationship may be observed between default and LTV. Since lenders may require lower LTVs in order to mitigate risk, mortgages with low and moderate LTVs may be as likely to default as those with high LTVs. Mindful of this risk endogeneity and its empirical implications, we examine the default experience of 495 fixed–rate multifamily mortgage loans securitized by the Resolution Trust Corporation (RTC) and the Federal Deposit Insurance Corporation (FDIC) during the period 1991–1996. The extensive nature of the data supports multivariate analysis of default incidence in a number of respects not possible in previous studies. Consistent with our expectations, we find that LTV evidences no relationship to default incidence, while the strongest predictors of default are property characteristics, including three–digit ZIP code location and initial cash flow as reflected in the debt coverage ratio. The latter results are particularly interesting in that they dominated the influence of postorigination changes in the local economy.     

Privatized Default Risk and Real Estate Recessions: The U.K. Mortgage Market

A mortgage pricing model is developed when a borrower goes through a series of distress states, including delinquency, long-term nonpayment and ultimate default. These steps are sequential, and depend on prices and alternatives faced by the borrower. The multistate default model is applied to the mortgage market in the United Kingdom. As a byproduct, a pricing structure for the U.K. endowment mortgage, which combines a good and a life insurance policy, is developed. Income and liquidity constraints are shown to affect the decision to keep a mortgage current in different states of distress. Solvent borrowers may thus keep their mortgages current, even when equity is negative.     

Equity Dilution: An Alternative Perspective on Mortgage Default

Empirical research on mortgage default in the single-family market has focused on the value of the borrower's put option using house price indices to estimate contemporaneous loan-to-value ratio or the probability of negative equity. But since the borrower possesses the option to increase leverage by taking on additional debt secured by junior liens subsequent to loan origination (a phenomenon termed here equity dilution ), even a perfect house price adjustment cannot be expected to accurately measure changes in borrower equity over time. Since junior liens are generally unobservable to senior debt holders, proxies are required in empirical applications. This paper employs an independent estimate of junior lien probability developed from the 1998 Survey of Consumer Finances combined with loan level mortgage performance data to examine the role junior liens play in increasing default risk.     

Pricing Default Risk in Mortgages

This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment. Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions. The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined. The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper.     

Commercial Mortgage Pricing with Unobservable Borrower Default Costs

This paper develops a pricing model for commercial real estate mortgage debt that recognizes the influence of default transaction costs on the borrower's default decision. These costs are heterogeneous across borrowers and largely un-observable to the lender/investor at the time of origination or loan purchase. A recognition of these unobservable costs can explain why borrower default decisions may differ from those predicted by "ruthless" mortgage-default pricing models. We address the determinants of default choice and timing by replacing sharp default boundaries found in the ruthless models with "fuzzy" boundaries that account for investor uncertainty with respect to evaluating borrower default decisions. To implement our model, we estimate probabilities of default as a junction of time and net equity in the property. Then, given that default occurs, loss severities are modeled based on expected property value recovery net of foreclosure costs and time until the asset is actually sold. Under reasonable parameter value choices, resulting Monte Carlo simulations produce numerical mortgage price estimates as well as component default frequency and severity levels that realistically reflect default premiums and loss levels observed in the marketplace.     

Estimation of Mortgage Defaults Using Disaggregate Loan History Data

This paper addresses, theoretically and empirically, the structure of influences affecting the default option in mortgage contracts. A formal theoretical model recognizes that a number of loan and non-loan related effects beyond equity in the unit could influence the default decision. These include 1) payment levels relative to income, which could displace other investment opportunities or cause a need for borrowing or sale to meet mortgage obligations; 2) current and expected neighborhood and housing market conditions, in particular the expected relative rate of appreciation of the unit and the relative cost of homeownership; 3) economic conditions; 4) wealth; 5) borrower characteristics proxying for variability in income or "crisis" events; as well as 6) transactions costs incurred upon default. Estimates of the model making use of a micro-level sample of individual loan histories over a twelve year period, supplemented by longitudinal census and economic information, find a number of these "other" effects important. Simulations find several of them to dominate the equity effect on default and to help explain why some households with zero or negative equity may not default, while others with positive equity may. The implications of these results for appropriate specification of the pricing model describing the default option and for appropriate underwriting of AMIs are noted.     

Semivariance of Property Value Estimates as a Determinant of Default Risk

Standard practice in the residential mortgage underwriting industry is to estimate collateral values via independent appraisals conducted by third parties. This paper empirically examines the role of property value ( i.e. , appraisal) uncertainty as a determinant of default on residential mortgage loans. Based upon an analysis of 1,428 residential loans drawn from the portfolio of a national mortgage lender, we find evidence that semivariance in property value uncertainty is related to default risk. Specifically, subject properties that are valued above the sales price of recently sold "similar and proximate" properties show evidence of greater default risk. Interestingly, a variance (range) measure of property value uncertainty is not significantly related to default risk.     

The Adjustable Balance Mortgage: Reducing the Value of the Put

We propose a new mortgage contract that endogenously captures the risk of house price declines to minimize default risk resulting from changes in the underlying asset value while still retaining contract rates near the cost of a standard fixed‐rate mortgage. By reducing the role of the legal system in mitigating house price risk, the new mortgage reduces the negative externalities and social costs arising from defaults. In other words, the new mortgage minimizes the need to use the legal foreclosure system to deal with the economic risk of house price declines.     

Modelling Mortgage Terminations in Turbulent Times

Techniques used to predict mortgage defaults during a relatively stable period proved less successful during the turbulent financial cycle of the early 1980s. An alternative specification of the relationship between defaults, homeowner equity, and interest-rate movements better captures the effect of interest rates on default probability. Results confirm the powerful effect of equity on mortgage defaults and the strong, but asymmetric, influence of interest rates on both defaults and prepayments. The new specification allows direct measurement of the interest-rate effect on defaults, distinguishing the effect when rates rise or fall.     

The Subprime Virus

We examine the correlation between prime mortgage default risk and the introduction of subprime mortgages in a local area. We motivate our analysis with a model of a default contagion effect that spreads the effect of a mortgage foreclosure from one property to surrounding properties. Through numerical analysis, we demonstrate the effect of subprime mortgage originations to the risk of prime mortgages. Finally, we offer empirical support for our model by examining the spatial variation in MSA prime mortgage default rates and the level of subprime mortgage activity.     

The Termination of Commercial Mortgage Contracts through Prepayment and Default: A Proportional Hazard Approach with Competing Risks

This article examines the factors driving the borrower's decision to terminate commercial mortgage contracts with the lender through either prepayment or default. Using loan–level data, we estimate prepayment and default functions in a proportional hazard framework with competing risks, allowing us to account for unobserved heterogeneity. Under a strict definition of mortgage default, we do not find evidence to support the existence of unobserved heterogeneity. However, when the definition of mortgage default is relaxed, we do find some evidence of two distinctive borrower groups. Our results suggest that the values of implicit put and call options drive default and prepayment actions in a nonlinear and interactive fashion. Prepayment and default risks are found to be convex in the intrinsic value of call and put options, respectively. Consistent with the joint nature of the two underlying options, high value of the put/call option is found to significantly reduce the call/put risk since the borrower forfeits both options by exercising one. Variables that proxy for cash flow and credit conditions as well as ex post bargaining powers are also found to have significant influence upon the borrower's mortgage termination decision.     

Regional Economic Stability and Mortgage Default Risk in the Netherlands

This paper investigates the relationship between regional economic diversification and stability, and residential mortgage default risk in the Netherlands. To describe and measure regional economic diversity and stability, methods from both the regional economics and the industrial economics literature are used. All measures are based on regional employment characteristics. Mortgage default rates were obtained from a database of the population of insured mortgage defaults in the Netherlands from 1983 through 1990. To test the relationship between the measures and mortgage default risk, cross sectional Seemingly Unrelated Regression was used. The paper concludes that the employed measures explain regional mortgage default rates to a significant extent, and that stability measures outperform diversity measures.     

Thy Neighbor’s Mortgage: Does Living in a Subprime Neighborhood Affect One’s Probability of Default?

This article focuses on the potential externalities associated with subprime mortgage origination activity. Specifically, we examine whether negative spillover effects from subprime mortgage originations result in higher default rates in the surrounding area. Our empirical analysis controls for loan characteristics, house price changes and alternative loan products. Our results indicate that, after controlling for these characteristics, the concentration of subprime lending in a neighborhood does not lead to greater default risks for surrounding borrowers. However, we do find that more aggressive mortgage products (such as hybrid adjustable rate mortgages and low/no‐documentation loans) had significant negative spillovers on other borrowers. Stated differently, the aggressive alternative mortgage designs were more toxic to the housing and mortgage market than previously believed.     

Waiting to Default: The Value of Delay

This paper analyzes the opportunity for early termination of a mortgage contract. We consider the possibility of defaulting on the property and explore the rules that are used by a value-maximizing borrower in exercising this option to default. The discussion centers on the value of waiting to make such a decision and the consequences of this rational inertia. We show that the observed delay in default usually attributed to transaction costs can instead be explained as entirely rational choice in a dynamic environment.     

Government Policies,Residential Mortgage Defaults and the Boom and Bust Cycle of Housing Prices

We develop a micro‐based macromodel for residential home prices in an economy where defaults on residential mortgages negatively affect housing prices. Our model enables us to study the impact of subprime defaults on prime borrowers and the impact of various government policies on the housing market boom and bust cycle. In this regard, our key conclusions are that (i) there is a contagion effect from subprime defaults to prime defaults due to the negative impact of subprime defaults and (ii) monetary policy is the most effective tool for decreasing mortgage defaults and increasing aggregate home prices in contrast to alternative government fiscal policies designed to loosen mortgage credit.     

The Role of Home Equity Lending in the Recent Mortgage Crisis

Home equity lending grew rapidly from 2000 to 2008 with balances more than tripling. In this article, we examine the role this phenomenon may have played in increasing aggregate default risk during the mortgage crisis. We also document a relationship between growth in home equity lending and high house price depreciation and first mortgage default during the downturn of 2006–2009. Line of credit growth is shown to be associated with large increases in nonowner‐occupied property purchases, suggesting that home equity lines of credit were tapped to fund such investments, exacerbating default rates during the market downturn.     

Evaluating the Costs of Increased Lending in Low and Negative Growth Local Housing Markets

The literatures on default and the evaluation of low downpayment mortgage programs are extended by showing within an options pricing framework how differences in expected price appreciation trends across housing markets can influence default and, thereby, the cost of programs designed to increase mortgage liquidity. An equilibrium mortgage rate reflecting the risk premium required to compensate for expected default-related losses is endogenously determined within the model. Evaluating the entire process by which program losses arise strictly within a rigorous asset pricing framework has potentially important implications for policy evaluation, as the estimated present value of program losses in declining markets where expected default is high is quite sensitive to the choice of the discount rate. The implications of increased lending in low and negative price appreciation local markets are also investigated.     

The Effect of Mortgage Payment Reduction on Default: Evidence from the Home Affordable Refinance Program

This article evaluates the effect of payment reduction on mortgage default within the context of the Home Affordable Refinance Program. We find that mortgage default is sensitive to payment reduction using univariate, duration and hazard modeling approaches. A relative risk Cox model of default with time‐varying covariates estimates that a 10% reduction in mortgage payment is associated with about a 10–11% reduction in monthly default hazard for loans. This finding is robust to the inclusion of empirically important mortgage risk drivers (such as current loan‐to‐value and FICO score) as well as controlling for selection effects based on observables.