A Dynamic Analysis of Fixed- and Adjustable-Rate Mortgage Terminations

This paper provides a side-by-side comparison of loan-level statistical models for fixed- and adjustable-rate mortgages. Multinomial logit models for quarterly conditional probabilities of default and prepayment are estimated. We find that the estimated impacts of embedded option values for prepayment and default are generally quite similar across both FRM and ARM loans, providing additional empirical support for the basic predictions of the options theory. We also find that differences in estimates of conditional probabilities of prepayment and default associated with mortgage age, origination period, original LTV, and relative loan size, indicate the continued significance of these other economic and demographic factors for empirical models of mortgage terminations.     

Omitted Mobility Characteristics and Property Market Dynamics: Application to Mortgage Termination

Property market dynamics depend on changes in long run equilibrium and on impediments to adjustment towards equilibrium. Mortgage termination due to mobility, default and refinancing provides a lens for evaluating property market adjustments. The borrower’s decision to move as an adjustment mechanism in the property market is associated with utility-maximizing decisions to either prepay or default on the mortgage. The optimal choice between these two termination events may depend on unobserved propensities related to change in income, job location, or family size, and substantial inertial forces including search costs, neighborhood change and attachment to an area. We propose a method for modeling variables determining the impact of mobility on mortgage terminations with imperfect household and loan level data. Since omitted variables contribute to moving decisions and therefore to mortgage prepayment and default decisions, utility functions for sale and default are correlated through these unobservable variables; thus, the IIA assumption of the widely used Multinomial Logit Model (MNL) is violated. Under such circumstances, econometric theory suggests that the Nested Logit Model (NMNL) is a better choice, which obviates the limitation of MNL by allowing correlation in unobserved factors across alternatives. Using loan level micro data, we find empirical evidence showing significant correlation between sale and default due to omitted borrower mobility characteristics. Our simulations find that NMNL out performs MNL in out-of-sample prediction. Improved predictions of moves and defaults are applicable to micro and macro analysis of the housing market system.     

Optimal Stopping and Losses on Subprime Mortgages

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.     

Differential default risk among traditional and non-traditional mortgage products and capital adequacy standards

We develop a framework to quantify credit risks of non-traditional mortgage products (NMPs). Ex ante probabilities of default are caused by willingness-to-pay and ability-to-pay problems and the high default rates for NMPs confirm that payment shock is a critical default risk indicator. Monte Carlo simulations are conducted using three correlated stochastic variables (mortgage interest rate, home price, and household income) under normal and stressed economies. Results confirm that the default risk of 2/28 and option ARM contracts requiring a minimum monthly interest payment have a greater probability of default than other mortgage products in all economic scenarios. Additionally, the credit risk of NMPs is primarily systematic risk, suggesting that these products should require higher risk-based capital. Due to the non-linear distribution of credit risk, even the advanced internal-based rating approach of the Basle II framework can understate the risk involved in these NMPs.     

The probability of fixed- and adjustable-rate mortgage termination

This article analyzes mortgage terminations using a national individual loan data set for the 1986–1992 period. The standard option-choice-theoretic framework is supplemented with variables to proxy for non-option-related termination determinants. Separate multinominal logit models are estimated for three mortgage types: 30-year FRMs, 15-year FRMs, and 30-year ARMs. The results indicate substantial differences in the response of the mortgage types to variables included in the model. FRM15 prepayments are the most responsive to prepayment option values; FRM30 prepayments are less responsive to option values and are dirven by local area housing market and economic conditions; ARM prepayment rates are higher but defeult rates are lower relative to the FRMs. A noteworthy finding is that teaser discounts reduce the likelihood of ARM defaults.     

Commercial Mortgage Workout Strategy and Conditional Default Probability: Evidence from Special Serviced CMBS Loans

This study recognizes that commercial mortgage default is not a one-step process and examines a previously under explored aspect in the whole default process, that is the stage between the initial delinquency and default. We distinguish the servicers’ behavior from the borrowers’ behavior. A multinomial logit model is applied to analyze the servicers’ choice of workout options and a proportional hazard model is applied to analyze the borrower’s default decision-making process under time-varying conditions. We find that cash flow condition is the most significant factor in the servicers’ decision making process. We also find that borrowers make default decisions based upon both the equity position in the mortgage and the cash flow condition in the space market. Key real estate space market variables, such as market-level vacancy rates, also provide useful information in explaining commercial mortgage defaults. We find that special service seems to be successful in reducing the probability that a troubled loan will default. Finally, sensitivity analysis shows nontrivial economic significance of the impact of explanatory variables, real estate market variables in particular have the most significant impact on the pricing of special-serviced loans.     

Appraisal Quality and Residential Mortgage Default: Evidence from Alaska

We empirically examine the effect of appraisal quality on subsequent mortgage loan performance using data from the high volatility housing market of Alaska in the 1980s. We develop measures of appraisal quality by computing the residual between a hedonic estimate of house value using available information from other appraisals compared to actual ex ante appraised value. We then estimate proportional hazard models of mortgage default and find that several measures of appraisal quality, particularly appraised value in excess of hedonic estimates, are significantly related to default risk. Using valuations subsequent to loan default, we are also able to evaluate how well house price indices perform in terms of estimating current loan-to-value and offer some additional evidence on the controversy over the role of net equity versus trigger events as determinants of mortgage default. We also show that defaults are related to ex ante measures of housing market conditions, with additional implications for underwriting policies and the current industry trend away from traditional appraisal and toward automated valuation.     

Identifying the determinants of mortgage default in Colombia between 1997 and 2004

This paper examines the relationship between mortgage default decisions and relevant observable variables in Colombia between 1997 and 2004. We estimate a discrete choice model of default using a panel of individual mortgage characteristics and payment information. We show that home prices and debt balances are the main determinants of mortgage default. We account for the presence of unobserved heterogeneity using Survey data and simulation techniques. Including controls for the distribution of income shows that income was not important but helps clarifying the relevance of mortgage leverage in the determination of the observed default rates.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias

A proportional hazards model with competing risks is specified and is extended to correct for the possibility of originator bias. The model is used to examine the ability of option-theoretic models of mortgage pricing to forecast commercial mortgage defaults. Among the findings, those especially of interest include the influence of contemporaneous loan-to-value and debt-service-coverage ratios on commercial mortgage default probabilities. The paper also finds that option-theoretic models of mortgage pricing are quite capable of producing default estimates that fit the actual default rates well, especially when the model is corrected for originator bias.     

The Hazard Rates of First and Second Defaults

This article examines hazards of repeated mortgage default, conditional on reinstating out of an initial default episode. Results indicate that subsequent default risk for reinstated borrowers is significantly greater than the risk of first default, especially during the first two years after a default episode. In addition, economic factors helpful in predicting first defaults are not helpful in predicting subsequent default episodes. This has important implications for mortgage investors and servicers as industry foreclosure avoidance efforts intensify.     

Subprime Loan Default Resolutions: Do They Vary Across Mortgage Products and Borrower Demographic Groups?

This paper examines default outcomes for subprime first lien loans during the recent subprime mortgage boom. It conducts this investigation in two phases. The paper first examines factors associated with pre-foreclosure outcomes for subprime mortgages in default. It then examines factors associated with different outcomes for loans that enter foreclosure. These factors include less understood elements such as mortgage product features and borrower demographics. The analysis is based on detailed loan-level data and employs multinomial logit models in a hazard framework. Results show that default resolutions vary with product features and borrower demographics. Adjustable rate and interest-only mortgages, and loans with low- or no-documentation are more likely to enter foreclosure proceedings, and, once in foreclosure, are more likely to become REO. The existence of junior liens increases the probability of the loan remaining in default. Owner-occupancy is associated with lower likelihood of foreclosure initiation and REO, and greater likelihood of curing default. Additionally, default outcomes are impacted by local legal, economic and housing market conditions, and the equity in the home.     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

Bias in estimates of discrimination and default in mortgage lending: The effects of simultaneity and self-selection

The common practices of estimating single-equation models of mortgage rejection to test for discrimination in mortgage markets or single-equation ex ante mortgage default equations to validate underwriting criteria produce biased and inconsistent parameter estimates. This is due to problems of simultaneous equations bias which arise because, in a world of imperfect information, mortgage terms are not exogenous to the rejection or default decision. In addition, mortgage default estimates are also subject to selection bias. Monte Carlo experiments are used to study the nature and extent of likely bias in single-equation estimation results. We find that rejection equation estimates indicate discrimination when none exists and that estimated coefficients of mortgage terms, such as the loan-to-value ratio, are also subject to significant bias in both rejection and default equations.     

Government intervention in the mortgage market: A study of anti-redlining regulations

This paper addresses the question of whether economic incentives exist for mortgage lenders to avoid or to minimize mortgage originations in neighborhoods inhabited primarily by low-income racial minorities. The Option Pricing Model is utilized to determine what mortgage borrower characteristics affect the market value of the mortgage contracts. It is found that existing laws do not enable mortgage lenders to vary either origination prices or mortgage terms so as to adjust for differences in the market values of mortgages. As a result, incentives are created for both the mortgage lender and the mortgage insurer to avoid originations and underwritings in areas with relatively high default probabilities. Various changes in mortgage lending regulations are suggested to eliminate these incentives, and the effects of alternative programs to subsidize mortgage borrowers with relatively high default probabilities are considered.     

Disparities in Mortgage Lending,Bank Performance,Economic Influence,and Regulatory Oversight

This study investigates factors affecting changes in the disparity of home mortgage denial rates between white and minority loan applicants in the U.S. during the period 1991–1997. We develop a two-stage least-squares regression model that incorporates applicant-level characteristics, neighborhood characteristics, regional economic data, and bank-specific data as explanatory variables. Some have argued that mortgage lenders were under increasing pressure from industry regulators to extend additional credit to minorities and low-income groups during the period under study. The model includes each institution's periodic CRA rating as a proxy for regulatory influence. An alternative explanation is that market forces, such as improvements in economic conditions and in bank financial condition and performance, affected default loss estimates and credit standards in a way that disproportionally benefited minority and low-income applicants. The empirical findings are consistent with the latter hypothesis. We conclude that policy makers should consider the impact of market factors when assessing the allocation of mortgage credit in a particular demographic market. The findings also underscore the importance of controlling for lender assessments of credit risk when evaluating compliance with CRA and fair lending statutes.     

Mortgage Default with Asymmetric Information

This article analyzes mortgage-market equilibrium when borrower default costs are private information. By applying the approach of Rothschild and Stiglitz (1976), it is shown that asymmetric information regarding default costs distorts the contract choices available in the mortgage market, preventing safe borrowers (those with high default costs) from fully satisfying their demand for mortgage debt. Large loans are available for a substantial interest-rate premium, but only risky borrowers find this premium worth paying. The article builds on an empirical literature designed to test the ruthless-default principle from option-based models of mortgage pricing. That literature provides evidence against ruthless behavior, suggesting that default costs play an important role in borrower decisions. The article takes a further step by arguing that such costs are private information, which has important implications for market equilibrium.     

Effects of Noise on Optimal Exercise Decisions: The Case of Risky Debt Secured by Renewable Lease Income

This paper considers the valuation and default exercise policy of risky coupon debt that is secured by a lease-encumbered noisy real asset. For parameter values used in our analysis, asset value noise is shown to reduce the value of waiting to default. Moreover, the borrower is shown to delay default exercise until the noisy signal of asset value is far into-the-money. This latter finding provides an information-based explanation for the apparent under-exercise of the mortgage default option that has been observed in the literature. An implication of this finding is that, if the claimholder recognizes that noise exists, but the empiricist—who is trying to compare observed exercise policy with that predicted by a noiseless model of asset prices—does not, a “sub-optimal” exercise policy may be inferred when in fact the policy is rational given the information available. This explanation is consistent with evidence from mortgage default studies as to why the observed default exercise boundary is lower than that predicted by standard theoretical option-based models.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

An Analysis of Mortgage Termination Risks: A Shared Frailty Approach with MSA-Level Random Effects

Investigating the residential mortgage defaults and prepayments has been the subject of research for the past three decades. The literature on mortgage default and prepayment is often used to inform credit risk policies and asset pricing strategies. This literature has evolved from the use of logistic regressions to the use of survival and frailty models that control for unobserved heterogeneity. In this paper, we apply a shared-frailty survival model to analyze the mortgage termination risks. In particular, we investigate whether mortgages originated in the same Metropolitan Statistical Area (MSA) share common unobserved factors and how these factors affect the mortgage termination risks. The paper demonstrates that MSA-level frailty, together with other risk factors, has significant effects on the probability of mortgage terminations risks.