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.     

Valuing the Mortgage Borrower's Prepayment Option

This paper investigates the value of the prepayment option that normally accompanies a fixed-rate mortgage. Using the two-state option-pricing model developed by Bartter and Rendleman, the paper presents simulations of prepayment option values using several sets of interest rate parameters. The sensitivity of the value of the option to changes in various aspects of the mortgage contract is assessed. Prepayments are not priced separately in the market from the underlying mortgage, so the paper investigates how the inclusion of a prepayment option affects the contract interest rate. Finally, there is reason to believe that any option-pricing model will overestimate the value of a mortgage prepayment option. The size of this bias is assessed indirectly and is found to be rather small.     

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.     

Subprime Refinancing: Equity Extraction and Mortgage Termination

This article examines the choice of borrowers to extract wealth from housing in the high-cost (subprime) segment of the mortgage market and assesses the prepayment and default performance of these cash-out refinance loans relative to the rate of refinance loans. Consistent with survey evidence, the propensity to extract equity is sensitive to the relative interest rates of other forms of consumer debt. After the loan is originated, our results indicate that cash-out refinances perform differently from non–cash-out refinances. For example, cash-outs are less likely to default or prepay, and the termination of cash-outs is more sensitive to changing interest rates and house prices.     

An Analysis of the Ex Ante Probabilities of Mortgage Prepayment and Default

Observed mortgage prepayment and default rates have been far different than the ruthless option exercise rates predicted by contingent claims models of mortgage pricing. The discrepancies have been attributed to both the competing-risk nature of prepayment and default and to transactions costs. This paper tries a different means of reconciliation. We introduce a third stochastic process, household income, into the usual pricing model that includes only the spot interest rate and the house price. The presence of income allows considering consumption-theoretic determinants of termination. The role of mortgage underwriting rules in restricting optimal prepayment is also explicitly modeled. Numerical ex ante prepayment and default rates based on the theoretical model come much closer to historical experience.     

Unobserved Heterogeneity in Models of Competing Mortgage Termination Risks

This article extends unobserved heterogeneity to the multinomial logit (MNL) model framework in the context of mortgages terminated by refinance, move or default. It tests for the importance of unobserved heterogeneity when borrower characteristics such as income, age and credit score are included to capture lender-observed heterogeneity. It does this by comparing the proportional hazard model to MNL with and without mass-point estimates of unobserved heterogeneous groups of borrowers. The mass-point mixed hazard (MMH) model yields larger and more significant coefficients for several important variables in the move model, whereas the MNL model without unobserved heterogeneity performs well with the refinance estimates. The MMH clearly dominates the alternative models in sample and out of sample. However, it is sometimes difficult to obtain convergence for the models estimated jointly with mass points.     

Mortgage Default and Prepayment Risks among Moderate‐ and Low‐Income Households

Using a unique sample of community reinvestment loans, we study the propensity of very low‐income households to terminate a mortgage and compare it to the outcomes for low‐income and moderate‐income households. The results indicate that, even within moderate‐ and low‐income segments, lower or very low income is associated with higher default and lower prepayment probabilities. In addition, depending on how low the borrower's income is, classic determinants of loan termination such as credit scores, the amount of equity in the home and local labor market conditions can have different impacts on default and prepayment probabilities.     

Optimal Sharing of Interest‐Rate Risk in Mortgage Contracts: The Effects of Potential Prepayment and Default

Much of the literature on the economics of mortgage markets has studied the fixed vs. adjustable‐rate mortgage choice made by individual borrowers. However, to decide if the outcome of such a choice is efficient or approximately so, it is necessary to explore the question of optimal risk‐sharing in mortgage contracts. But because only a small literature has studied this question, more research is clearly warranted. The present article helps fill this gap by developing a simplified version of Arvan and Brueckner's model, using it to characterize optimal contracts in the absence of mortgage termination, and then exploring how termination via prepayment or default affects optimal risk‐sharing. The broad conclusion of the analysis is that potential mortgage termination makes higher risk exposure for borrowers optimal.     

Adjustable and Fixed Rate Mortgage Termination, Option Values and Local Market Conditions: An Empirical Analysis

This paper analyzes the probabilities of prepayment or default for Fixed Rate Mortgages (FRMs) and Adjustable Rate Mortgages (ARMs). Using data from the period 1985–1992, the analysis indicates that the likelihood of prepayment of thirty year FRMs was determined primarily by house price appreciation and personal income growth and the likelihood of prepayment of fifteen year FRMs was determined primarily by interest rate changes. ARMs were prepaid less frequently than FRMs, were less likely to be prepaid when interest rates declined and defaulted more often than FRMs. The analysis provides evidence that ARM holders are less mobile than FRM holders.     

Movers and Shuckers: Interdependent Prepayment Decisions

We model competing risks of mortgage termination where the borrower faces a repeated choice to continue to pay, refinance the loan, move or default. Most previous empirical work on mortgage prepayment has ignored the distinction between prepayments triggered by refinancing and moving, combining them into a single prepayment rate. We show that financial considerations are the primary drivers of the refinance choice while homeowner characteristics have more influence on the move decision. We demonstrate that these differences are statistically significant and that combining these two distinct choices into a single measure of prepayment shifts coefficients toward zero and produces inaccurate predictions of aggregate termination rates. For example, a combined model underestimates the effect of the market price of the loan on refinancing; it misses entirely the opposite effects of borrower income on moving and refinancing. Our results suggest that existing prepayment models are inconsistent predictors of mobility-driven prepayment and underestimate the effect of market conditions and borrower characteristics on refinancing and housing decisions. Our findings have great significance to mortgage investors because mobility-driven prepayments are likely to be a more significant source of prepayments in thenext decade.     

Prepayment Penalty as a Screening Mechanism for Default and Prepayment Risks

The objective of this article is to offer a theoretical model of asymmetric information to analyze the screening role of prepayment penalty. We consider both default risk and prepayment risk. What makes the role of prepayment penalty interesting and more complicated is that a borrower's contract choice could send conflicting signals to the lender about that borrower's default and prepayment risk type. This is different from earlier theoretical models of mortgage choice under asymmetric information where a certain aspect of the contract (e.g., discount points or loan‐to‐value ratio) is explored as a screening mechanism for a single risk dimension (default risk or prepayment risk) of the borrower type. We show the existence of separating equilibria where different default and prepayment risk types choose contracts with different combinations of prepayment penalty and interest rate. For certain parameter combinations, the model also generates a pooling equilibrium where all borrower types obtain the same contract. Our analysis could offer a partial explanation for the observation that contracts with prepayment penalties are a lot less prevalent than contracts with points.     

Reverse Mortgages and Prepayment Risk

This paper presents a detailed assessment of the Connecticut Housing Finance Authority (CHFA) reverse annuity mortgage (RAM) program. Because of the size and payment history of the program, the analysis provides an empirical framework on which to develop and assess other home equity conversion (HEC) programs. The program offers insights into the economic impact of these programs and the factors affecting prepayment. The program issued 765 annuities over five years, and 240 of these loans have terminated payments. The annuity payments had a demonstrable financial impact on the elderly participants, with an 88% average annual income increase. Prepayment rates varied across borrower and loan characteristics. The rates were most sensitive to marital status and were heavily affected by the age of the borrower and the term of the loan. Although default risk exists, the evidence indicates a low probability of the loan value exceeding the house value.     

Housing Price Dynamics,Mortgage Credit and Reverse Mortgage Demand: Theory and Empirical Evidence

This article presents some theoretical and empirical approaches for identifying interactions among fundamental economic variables that determine housing prices. Using home equity conversion mortgage (HECM) loan‐level data, this study quantifies the major risks of reverse mortgages and shows that higher housing prices induce higher demand for reverse mortgages among elderly homeowners. Senior citizens rationally hold pessimistic expectations about future housing price appreciation and lock in their home‐equity gains by obtaining reverse mortgages, which in turn led to the substantial HECM growth prior to the financial crisis of 2008. A novel simulation also forecasts HECM loans under various economic scenarios. From a mortgage credit perspective, these findings generate several policy implications for the implementation of “HECM 3.0.”     

Prepayment Behavior of Dutch Mortgagors: An Empirical Analysis

The suboptimal exercise of the prepayment option in a mortgage is relevant for mortgage pricing and the management of a mortgage portfolio. Construction of an accurate prepayment model requires quantification of driving factors such as seasoning, seasonality, refinance incentive and burnout. We focus on Dutch mortgages but also discuss the Dutch market in a European setting. Within the euro-denominated MBS market, the Dutch market is often referred to as the benchmark market. In our application we include typical Dutch market and contract characteristics such as the annual penalty-free prepayment of 10 to 20% of the original loan amount. We use loan-level historical data on mortgages originated between January 1989 and June 1999 to estimate separate models for two popular redemption types: savings mortgages and interest-only mortgages. In both models we allow for suboptimal prepayment behavior. The results clearly indicate that prepayment rates depend on interest rates and the age of the mortgage contract. Moreover, we find that burnout is an important element in describing the prepayment behavior of Dutch mortgagors.     

Residential Mortgage Markets and the Cost of Mortgage Funds

Early federal housing finance policy appears to have been largely directed at making mortgages more marketable. The creation of FHA, FNMA and FHLMC were designed to homogenize the mortgage instrument and to develop a secondary market for it. Apparently because of a lack of demand for marketability by investors, extensive trading of mortgages has not developed. Nonetheless, the fantastic growth in mortgage pools (as well as the unanticipated growth in FNMA holdings) has increased competition in the supplying of some intermediation functions (mortgage bankers have greatly expanded originations and servicing), has improved interregional flows of mortgage funds, and has given mortgage borrowers a greater access to capital markets generally. The principal result has been a decline in the mortgage rate relative to other market rates, although the inflation-triggered explosion in the demand for mortgage funds in recent years appears to be offsetting the impact of the growth in federal credit broadly defined.     

UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation

We use a mean-reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lender's coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lender's (residual) exposure to house price risk, given the borrower's options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages.     

Mortgage Markets and Inter-Regional Differences in Conventional Mortgage Terms

One of the purposes of the secondary mortgage market is to move funds from areas of capital surplus to areas of capital shortage. If mortgage funds move freely throughout the economy then the price of mortgage funds (the terms of the mortgage) should be the same everywhere. Thus, if the secondary mortgage market is efficient, mortgage terms should show less geographic variation after the secondary market began in 1970 than they showed before. In this paper, the efficiency of the market is tested in two stages. In the first, the average terms of mortgage loans in 1968 and 1978 are examined to determine whether they became more homogeneous after the secondary market was begun. In the second stage, the terms are modeled as a function of region, year by region interaction variables, foreclosure rates, the usury ceiling and the average cost of funds. This model is estimated and analyzed using a multivariate multiple regression technique.     

Mortgage Pass-Through Securities: Progress and Prospects

This paper discusses the Housing Commission's perspective and recommendations on mortgage pass-through securities markets, reviews federal policy toward such securities in the wake of the Housing Commission Report , and considers prospects for mortgage securities in the housing finance system of the future. Concerning the outlook, it is concluded that massive "securitization" of housing finance may not be inevitable–contrary to the developing conventional wisdom on this topic–partly because the underlying need for secondary market transactions may not be as strong as commonly expected. Furthermore, the relative importance of pass-through securities as secondary market vehicles may erode if federally related programs are phased down in line with Housing Commission recommendations, even if policies currently being developed within the Administration to improve the functioning of fully private securities markets are implemented.     

Pay Me Now or Pay Me Later: Alternative Mortgage Products and the Mortgage Crisis

Mortgage contract design has been identified as a contributory factor in the recent market crisis. Here we examine alternative mortgage products (including interest‐only and other deferred amortization structures) and develop a game theoretic model of contract choice given uncertain future income and house prices across different types of borrowers. Results imply that deferred amortization contracts are more likely to be selected in housing markets with greater expected price appreciation and by households with greater risk tolerance; moreover, such products necessarily entail greater default risk, especially among lower‐income households who are aggressive in housing consumption levels. Empirical tests of model predictions generally provide support for the theory.