Mortgage Choice: What's the Point?

This article shows that, in the presence of transaction costs payable by borrowers on refinancing, it is possible to construct a separating equilibrium in which borrowers with differing mobility select fixed rate mortgages (FRMs) with different combinations of coupon rate and points. We also show that, in the absence of such costs, no such equilibrium is possible. This provides a possible explanation for the large menus of FRMs typically encountered by potential borrowers, and suggests that the menu available at the time of origination should be an important predictor of future prepayment. We numerically implement the model, developing the first contingent claims mortgage valuation algorithm that can quantify the effect of self-selection on real contracts in a realistic interest rate setting. The algorithm allows investors to account for self-selection when valuing mortgages and mortgage-backed securities. It also, for the first time, allows lenders to determine the optimal points/coupon rate schedule to offer to a specified set of potential borrowers, given the current level of interest rates.     

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.     

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.     

Pricing Mortgage Originations

The general structure of observed mortgage loan contracts and the structure of firms in the industry can be explained in terms of competitive markets and rational expectations. It is not necessary to invoke disequilibrium, credit-rationing theories. Collateralization, covenants, downpayments, and other noninterest rate provisions in loan contracts are efficient mechanisms to control the conflict of interest between the borrower and lender. Finally, there are constraints lenders place on the range of contractual provisions offered because of interdependencies in payoffs across contracts and the costs they face associated with insolvency.     

Financial Literacy,Broker–Borrower Interaction and Mortgage Default

This article examines the relationship between broker–borrower interaction in the origination process and subsequent mortgage performance. I show that face‐to‐face interaction between a mortgage broker and borrower before the loan funds is associated with lower levels of ex post default. The relation between face‐to‐face broker–borrower interaction and mortgage performance holds only for borrowers that have characteristics associated with low levels of financial literacy. Specifically, face‐to‐face interaction is negatively related to default for minorities, borrowers located in areas with low levels of education, low‐income borrowers and borrowers with low FICO scores. My results suggest that face‐to‐face interaction between the mortgage broker and borrower may reduce problems associated with financial illiteracy.     

Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages

This paper integrates two fundamentally important parameters into a theory of optimal mortgage design: the proportion of inflation risk borne by the lender / investor and the borrower and the amortization-graduation schedule for loan repayments. Equations are derived for a family of innovative mortgages, termed hybrid PLAMs, which offer advantages to borrowers and lenders over either the standard fixed rate mortgage (FRM) or the price level adjusted mortgage (PLAM). The superiority of the hybrid PLAMs lies in their ability to simultaneously and independently accommodate differing degrees of inflation-risk sharing and payment affordability. Inflation-risk sharing is represented by an indexation parameter set over a continuum of values such that the FRM has zero index variability and the PLAM has unit index variability. Similarly, payment tilt is represented by a tilt parameter such that the FRM has zero tilt and the PLAM has unit tilt. We demonstrate that these two parameters are independent and can each be continuously varied in a two-dimensional family of self-amortizing mortgages. A specific hybrid PLAM can be designed to partition inflation risk in any proportion between the borrower and the lender and to simultaneously prescribe any level of payment tilt between the extremes of the FRM and PLAM. The behavior of representative hybrid PLAMs is simulated and compared to FRMs and PLAMs for three different inflation scenarios, one of which uses actual market data from the period of 1960–1990.     

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.     

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.     

Mortgage Refinancing with Asymmetric Information

Information asymmetry exists between the lender and the borrower regarding the holding period of the mortgaged real estate; the lender does not know how long the borrower plans to own the house. This information asymmetry allows the cost of obtaining a mortgage to deviate from its value to the borrower. As a result, the exercise price of the option to refinance becomes the cost to the borrower of obtaining a new mortgage instead of the outstanding balance of the existing mortgage as used in previous models. The option to refinance is a sequential option; after the borrower refinances, a new option is obtained to refinance again in the future. A mortgage refinancing model is developed taking information asymmetry and sequential refinancing into account. The model is used to solve for (1) the value to the borrower of a callable mortgage and (2) the minimum interest rate differential between the contract rate of the existing mortgage and the market interest rate needed to justify refinancing.     

Lender Steering in Residential Mortgage Markets

In this article, we examine the incentives for lenders to steer borrowers into piggyback loan structures to circumvent regulations requiring primary mortgage insurance (PMI) for loans with loan‐to‐value ratios (LTV) above 80%. Our empirical analysis focuses on propensity score‐matched portfolios of piggyback and single‐lien loans having the same combined LTV based on a full set of observed risk characteristics. Our results confirm that mortgages originated with the piggyback structure have much lower ex post default rates and faster prepayment speeds than corresponding PMI loans. We also find a significant causal effect of interstate banking deregulation on the growth of piggybacks in these years, confirming that the ex post performance gap is primarily driven by lender steering on the supply side and not by borrower self‐selection. We then perform a number of tests to explore different origination and execution channels of mortgage steering.     

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.     

Temporary Buydowns and Affordability

This paper is directed to a neglected aspect of the problem of home ownership affordability: the impact on affordability of temporary buy downs. A temporary buydown is an option offered to home buyers to reduce the mortgage payment in the early years of the loan. The borrower allocates cash up front to an escrow account from which funds are withdrawn monthly to supplement the borrower's mortgage payment.
Temporary buydowns are underused partly because of the difficulty of determining whether, in any particular case, they will increase affordability. This paper develops a new instrument called the maximum affordable mortgage (MAX) which automatically allocates the buyer's available cash between buydown, down payment and other uses in a manner which maximizes affordability for the buyer, subject to whatever underwriting constraints the investor wishes to impose on payment graduation and/or the total size of the buydown.
The lender originating the MAX must be able to solve a complex algorithm at the point of sale, but the complexity is all behind the scenes. Using a computer, a loan officer can quickly find the cash allocation that maximizes affordability. The power of the MAX in increasing affordability may be enhanced if it is combined with a buyup wherein the lender trades off lower points against a higher rate.     

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.     

Why Do We Have ARMs?

This paper suggests a resolution to the paradox of inefficient risk bearing by adjustable-rate mortgage (ARM) borrowers. The analysis shows that when contracts are written in a realistic way, with payments linked across time via a common loan-rate function, risk sharing and the tilt of the mortgage payment stream become inextricably linked. Unless time preferences are identical or the cost of funds exhibits no time trend, borrowers will accept interest-rate risk in order to gain a more favorable time path of mortgage payments.     

Mortgage Borrower Repayment Behavior: A Microeconomic Analysis with Canadian Adjustable Rate Mortgage Data

In this paper we estimate a model of mortgage borrower behavior using micro-level data on Canadian borrowers with rollover mortgages—a form of adjustable-rate mortgage. Our results suggest that the probability of default rises with a decrease in housing equity and an increase in the mortgage contract rate; however the size of these changes is relatively small. They also show that partial prepayment is sensitive to fluctuations in the rates of return from investing in housing versus other assets. For the United States experience, our results suggest that, relative to fixed-rate mortgage borrowers, adjustable-rate mortgage borrowers are more likely to default and less likely to prepay.     

Risk and the Home Equity Conversion Mortgage

This article analyzes the risks involved with reverse mortgage insurance and explains the pricing model developed for the Home Equity Conversion Mortgage (HECM) demonstration. The paper demonstrates how borrower longevity, interest rates and property value changes all affect pricing, and why the HECM model focuses on property value as the primary source of uncertainty. It goes on to explain why a random walk specification was chosen to forecast property values, and how the principal limit factors, which determine cash payments to borrowers in the HECM program, are calculated.     

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.     

Mortgage Shoppers: How Much Do They Save?

Survey evidence suggests that many U.S. and European consumers do not spend a lot of time comparing mortgage products. We show, however, that mortgage shopping is associated with a substantial monetary payoff, using a unique data set from a website where borrowers (not the lenders) can post their complete set of received mortgage rate offers. A borrower who shops for five mortgage offers is able to save 7,078 euros in net present value on average. The potential savings suggest suboptimal mortgage shopping as the opportunity cost of time to renegotiate additional quotes is unlikely to be that high.     

Servicer Contracts and the Design of Mortgage‐Backed Security Pools

We develop a unified model of mortgage and servicer contracts. Renegotiating mortgage contracts following default is strictly Pareto improving, if the lender gathers updated information. An incentive compatible servicer contract requires the servicer to hold a risk position that has a value strictly greater than the cost of exerting effort. This risk position cannot in general be approximated with a horizontal “first‐loss” position. An alternative, forming a nondiversified pool, preserves pool‐wide information, avoids the cost of an incentive compatible servicer contract, and may increase MBS value.     

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.