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.     

Reverse Mortgages: Contracting and Crossover Risk

A pricing model is developed for a reverse mortgage contract where the borrower receives payments either as a lump sum or in an annuity while the loan balance accumulates as a claim against the house. No underwriting criteria on income are applied. One risk of default is that the borrower will remain in the house after the negatively amortizing loan balance exceeds the value of the house. An explicit pricing model of the reverse mortgage permits the evaluation of this default "crossover" option. Alternative methods involving life insurance contracts and securitization are compared as secondary market channels.     

On the Assessment of Default Risk in Commercial Mortgage Lending

This paper takes an initial step toward the development of an empirically-based model of default risk assessment in the commercial mortgage market. A review of existing empirical studies of residential mortgage and commercial loan default provides evidence for appropriate model specification and estimation. A simple default risk model for commercial mortgages is then developed based upon the generalized default risk models of Jackson and Kaserman [1980] and Vandell [1981]. The model is then examined for its ability to successfully handle a variety of situations and used to test the validity of traditional ratio analysis "rules-of-thumb" employed in commercial lending. Ratio tests are found generally to be inconsistent with an objective of constraining default risk below some maximum. Finally, a modified ratio analysis consistent with the model and with a constrained default risk strategy is introduced.     

Green Buildings in Commercial Mortgage‐Backed Securities: The Effects of LEED and Energy Star Certification on Default Risk and Loan Terms

We study the impact of green building on loans in the CMBS market. A hazard model shows green buildings carry 34% less default risk, all else equal. A matched‐sample analysis gives similar results. We attribute the effect to a loan‐to‐value channel, where risk is lowered by a green price premium. The benefit comes at least partly from the level of green achievement, not only the label itself. Loans on buildings that were green at loan origination have slightly better terms than loans on nongreen buildings. That difference is growing over time, but the effect is economically small compared to default risk.     

Contemporaneous Loan Stress and Termination Risk in the CMBS Pool: How “Ruthless” is Default?

This study analyzes the impact of contemporaneous loan stress on the termination of loans in the commercial mortgage‐backed securities pool from 1992 to 2004 using a novel measure, based on changes in net operating incomes and property values at the metropolitan statistical area‐property‐type‐year level. Employing a semi‐parametric competing risks model for a variety of specifications, we find that the probability of default is extremely low even at very high levels of stress, although the coefficient estimates of greatest interest are very statistically significant. These results suggest substantial lender forbearance and are consistent with previous research that models default as a “gradual dynamic process” rather than a “ruthless” exercise once “in the money.”     

The Impact of Second Loans on Subprime Mortgage Defaults

An estimated 12.6% of primary mortgage loans were simultaneously originated with a second loan from 2004 until 2008, although relatively little is known about how the presence of such subordinate loans affects the default decisions of borrowers. We use a novel data series of loan servicing records from 2002 until 2010 to identify such borrowers and find evidence that the default behavior of these borrowers significantly differs from borrowers without second loans. Estimating a discrete‐time proportional odds hazard model, we find borrowers with a second loan were 62.7% more likely to default each month on their primary loan when conditioning alone on the attributes of the primary loan. However, borrowers of second loans were 58.3% less likely to default on their primary loan as compared to single‐loan borrowers with equivalent current combined attributes (i.e., loan‐to‐value, balance and interest rate). We hypothesize and provide empirical evidence that this occurs because borrowers with second loans have the option to sequentially default on each loan since subordinate lenders will not pursue foreclosure if borrowers have insufficient equity. Lenders of defaulted subordinate debt may revisit their decision to foreclose in the future after housing markets start to recover, thus prompting a new round of foreclosures.     

Mortgage Lending, Sample Selection and Default

Traditional models of mortgage default suffer from sample-selection bias because they do not control for the loan approval process. This paper estimates a sample-selection-corrected default model using the 1990 Boston Federal Reserve loan application sample and the 1992 Federal Housing Authority (FHA) foreclosure sample. A single-equation FHA default model appears to suffer from substantial selection bias, but the bias primarily arises from the omission of credit history and other variables that are only in the application sample. Therefore, default models that contain detailed information on applicants may not suffer from substantial selection bias. Finally, a test for prejudice-based discrimination is developed and conducted, but the findings are inconclusive.     

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.     

Mortgage Prepayment and Default Decisions: A Poisson Regression Approach

This paper uses an extensive and geographically dispersed sample of single-family fixed rate mortgages to assess the prepayment and default behavior of individual homeowners. We make use of Poisson regression to efficiently estimate the parameters of a proportional hazards model for prepayment and default decisions. Poisson regression for grouped survival data has several advantages over partial likelihood methods. First, when dealing with time-dependent covar-iates, it is considerably more efficient in terms of computations. Second, it is possible to estimate full-hazard models which include, for example, functions of time as well as multiple time scales (i.e., age of the loan and calendar time), in a much more straightforward manner than partial likelihood methods for un-grouped data. Third, Poisson regression can be used to estimate non-proportional hazards models such as additive excess risk specifications. Taken together, our data and estimation methodology allow us to obtain a better understanding of the economic factors underlying prepayment and default decisions.     

Industrial Real Estate Mortgage Default Experience of the New York State Job Development Authority Second Loan Program: A Preliminary Investigation

This paper explores the loan loss experience of a public industrial lending authority, employing contemporaneous borrower net equity as a link to mortgage loan default. The relationship between default, net equity and bankruptcy is tested on a small longitudinal data set of loans using nonparametric statistics and a proportional hazard model. Results show that negative net equity and firm bankruptcy are strongly associated with default among the study population. Further, the borrowers studied did not exercise the put option promptly, suggesting potential benefits from monitoring net equity one year or more prior to default.     

Predicting Commercial Mortgage Foreclosure Experience

This study has two objectives: (1) it directly evaluates the relationship between commercial mortgage default incidence and characteristics of the mortgage, borrower, property, market, and general economic conditions, and (2) it uses this relationship to predict the exposure of life insurers to future mortgage defaults and to examine the relative importance of various causes of current and past credit quality problems. A theoretical model of the default decision predicts that the decision would be expected to be driven primarily by the borrower's current equity stake in the property, or the ratio of the market value of the loan to property value (M_t/V_t), but that the presence and magnitude of transaction costs associated with default would be expected to result in underexercise of the default option. Empirical estimation making use of American Council of Life Insurance (ACLI) and National Council of Real Estate Investment Fiduciaries (NCREIF) data confirms both expectations. A high proportion of the longitudinal variation in foreclosure incidence is explained by variations in M_t/V_t, but even at high ratios M_t/V_t in excess of 1.1. only 5% to 8% of mortgagors default, although this magnitude of underexercise is probably overstated because of problems in measuring M^t and for other reasons. Simulations using the model provide a pessimistic outlook for future defaults. Default rates are predicted to double in the five-year period 1988–93. Other simulations examine the relative importance of interest rate fluctuations, property value declines, and geographic or temporal correlations in lending during the 1976–88 period on current default experience.     

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.     

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.     

Handing Over the Keys: A Perspective on Mortgage Default Research

This paper is the text of the 1992 Presidential Address for the American Real Estate and Urban Economics Association. A comparative evaluation of mortgage default research finds that both the residential and commercial markets evolved from informal underwriting rules, to formalized (though unvalidated) ratios and rules of thumb, to early risk ratings based upon empirical evidence, to gener-alizable econometric models of default, to option-based pricing models. The commercial market lagged the residential market by about 10 to 20 years at first but is now only about five years behind. The survey finds that research and progress in understanding mortgage credit risk has been precipitated by a public policy need or mandate, data availability, and adequate technology. The absence of any one of these factors has hindered progress in the past. Finally, six emerging issues in default research are identified and discussed: (1) the degree of "ruth-lessness" with which default is exercised, (2) loan recourse, (3) the magnitude and timing of revenues and losses associated with default, (4) loan modification, (5) default in a portfolio context, and (6) leasehold default. Progress in these areas will enhance the efficiency of both the residential and commercial markets.     

浅析利率调整对住房抵押贷款违约风险的影响

住房贷款利率的变化对房地产价格产生着巨大影响,房地产价格又是住房抵押贷款中重要因素,与住房抵押贷款风险密切相关。违约风险是住房低押贷款风险中最基本最主要的风险,也称信用风险。论文将从理论上分析利率政策调整对住宅抵押贷款违约风险的影响,并提出相应的防范措施。     

Do Riskier Borrowers Borrow More?

Conventional wisdom in the mortgage industry holds that loan-to-value (LTV) ratios are positively correlated with mortgage default rates. However, not all empirical studies of mortgage loan performance support this view. This paper offers a theoretical signaling model of why the correlation between LTV ratios and default risk is contingent upon the default costs of the borrower. Specifically, the model proposes that when default costs are high there exists a separating equilibrium in which risky borrowers will self-select into lower LTV loans to reduce the probability of facing a costly default, while safe borrowers will self-select into higher LTV loans as a signal of their enhanced creditworthiness. This adverse selection process gives rise to the possibility of higher default probabilities for lower LTV loans. Conversely, when default costs are low the conventional result, in which risky borrowers select higher LTV loans than safe borrowers, is obtained. Empirical results, based on a sample of 859 single-family residential mortgage loans drawn from the portfolio of a national mortgage lender, are consistent with the separating equilibria predicted by the model.     

The Impact of Interstate Foreclosure Cost Differences and the Value of Mortgages on Default Rates

Previous research on mortgage default has focused on the costs, benefits, and characteristics of the mortgagor. In such studies default rates have been taken as a measure of mortgage risk. In this paper we present a model where the position of the lender affects the default-foreclosure process. Important to the lender's decision to foreclose rather than renegotiate an existing loan are the value of mortgage and the legal costs associated with foreclosure.
The empirical evidence supports the hypothesis that both the value of the mortgage and legal foreclosure costs affect the foreclosure rate. In those states where legal foreclosure costs are high rates are significantly less than where costs are low. This suggests that previous models which include only the costs and benefits of default to the borrower are incomplete and that foreclosure rates can not be taken as a strict measure of mortgage risk. That is, low foreclosure rates may indicate that losses occur in other forms of loan negotiation rather than in expensive legal costs.     

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.     

Credit Rationing and Government Loan Programs: A Welfare Analysis

Asymmetric information about borrower default probabilities may lead to inefficient credit rationing of low-risk borrowers in otherwise competitive markets. In a simple model having these properties, we show that some types of government loan programs, such as loan guarantees issued through lenders, might improve economic efficiency. But the incentive for high-risk borrowers to misrepresent their loan quality is worsened by other government loan programs, notably those that try to target aid directly to rationed borrowers. As such, cost-effective programs may increase inefficiency. This surprising result highlights the need to conduct model-specific policy analyses, as opposed to analyses based on model-free performance indicators.