A Comparison of the Reinvestment Risk of the Price Level Adjusted Mortgage and the Standard Fixed Payment Mortgage

The purpose of this paper is to increase the understanding of the risk of the indexed mortgage, commonly referred to as the price level adjusted mortgage (PLAM). This is accomplished by comparing, analytically, the reinvestment risk of the PLAM and the standard fixed-payment mortgage (FPM) under conditions of stochastic inflation and real interest rates. The conclusion is that the PLAM has less reinvestment risk. From the viewpoint of an investor concerned with periodically reinvesting payment streams, the PLAM is the superior mortgage.     

A Simple Model of Mortgage Insurance

This paper uses a two-period model to analyze the borrower's choice of an optimal time pattern of mortgage payments in a world where future house values are uncertain. Since a decline in values can make the borrower's equity negative, leading to default on the mortgage, lenders in the model will require the purchase of mortgage insurance. The premium on the insurance policy will depend on the riskiness of the mortgage, which in turn depends on the magnitude of the initial mortgage payment. Mortgages with large (small) first payments will carry low (high) insurance premiums. Taking this fact into account, the borrower decides on the optimal riskiness of his mortgage. Borrowers who discount the future heavily choose risky mortgages carrying high insurance premiums, while those who place a higher value on future consumption opt for less risky contracts carrying low (or zero) premiums.     

Alternative Mortgage Instruments, Qualification Constraints and the Demand for Housing: An Empirical Analysis

Government-guaranteed mortgage loans (GFRMs) and adjustable-rate mortgages (ARMs) were introduced to make payment to income (PTI) and loan-to-value (LTV) qualification conventions less restrictive. This paper analyzes the effect of GFRMs and ARMs on the demand for housing. Using a large national data set for the 1988 to 1989 period, we employ a two-stage procedure to estimate housing demand. In the first stage, a multinomial logit model estimates the probability of choosing an FRM, ARM or GFRM. Predicted values from the logit are used to construct user costs and estimate housing demand. Using the model estimates, we simulate demand under four different mortgage availability regimes: FRM, FRM and GFRM, FRM and ARM and all three. These simulations indicate that GFRMs, by relaxing LTV constraints, increase housing demand by approximately 6.2% relative to the FRM regime; the addition of ARMs, by relaxing both PTI and LTV constraints, raises demand by an additional 6%, for a total of 12.2% with inclusion of all alternatives.     

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.     

Optimal Mortgage Refinancing with Stochastic Interest Rates

The purpose of this paper is to develop a dynamic model of mortgage refinancing in a contingent claim framework that simultaneously solves for the borrower's optimal mortgage refinancing strategy, the value of the refinancing call option, the value of the mortgage liability to the borrower, and the market (lender) value of the fixed-rate contract. We also calculate the minimum differential between the contract rate on the existing mortgage and the current interest rate that is required to trigger an optimal mortgage refinancing.     

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.     

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.     

Elective Mortgage Prepayment: Termination and Curtailment

Mortgage-prepayment risk underlies the structuring of mortgage-backed derivative securities, such as tranched real estate mortgage investment conduits. This prepayment comes either from mortgage termination or from curtailment, where the borrower retains the existing mortgage and prepays a portion. There are differences in cash flows from the two types of prepayment. In termination, the loan disappears from a pool, and the scheduled payment to investors in the pool is reduced. In curtailment, the loan survives, and the scheduled payment is unchanged but the term is reduced. There are implications for structuring mortgages and derivative securities. The prepayment decision is embedded in an in-tertemporal household utility maximization framework where choices are made between refinancing, making the regular payment, default or curtailment. Empirical results are presented for Government National Mortgage Association (GNMA) pools, and an algorithm is presented that separates the termination and curtailment components, facilitating the development of derivative securities.     

A Contingent Claims Analysis of Price Level-Adjusted Mortgages

This paper examines the performance of alternative mortgage instruments in an environment of stochastic price fluctuations. The two most widely discussed contracts that deal with inflation are the adjustable-rate mortgage (ARM) and the price level-adjusted mortgage (PLAM). The former compensates for inflation by paying the nominal interest rate, which contains a component reflecting the rate of inflation. Nonetheless, even without explicit nominal amortization, this results in real amortization and hence a tilting effect. In addition, the inflation component of the nominal interest rate is shown to reflect only anticipated and not actual inflation, and so the real value of an ARM fluctuates due to unanticipated inflation. A PLAM suffers from none of these defects. To the extent that one is interested in a mortgage whose properties reflect the underlying real environment, the price level-adjusted mortgage is the ideal instrument.     

Modeling the Conditional Probability of Foreclosure in the Context of Single-Family Mortgage Default Resolutions

Both empirical and pricing-simulation models of mortgage default focus on foreclosure in a one-step decision framework. Such models are misspecified to the extent that mortgage default and foreclosure are two separate decisions or events, where foreclosure is but one outcome of a default episode. This study examines the dynamics of mortgage borrower default episodes using a large sample of FHA-insured single-family mortgages. We estimate the influence of borrower characteristics, mortgage terms, and economic conditions on probabilities of various resolutions, highlighting under what conditions foreclosure is more likely to result from mortgage default.     

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.     

Home Ownership,Household Leverage and Hyperbolic Discounting

I examine tenure and mortgage choice in an equilibrium model in which households make decisions as if they discount hyperbolically rather than exponentially. Overall, hyperbolic discounting does not seem to explain the high rates of home ownership or portfolio concentration in housing in the data. I then study the choice between mortgages that require a substantial down payment and mortgages that require no down payment. Allowing households access to no‐down‐payment mortgages exacerbates rather than mitigates the undersaving of hyperbolic discounters. However, even when households discount hyperbolically, welfare is higher when households have access to no‐down‐payment mortgages.     

Preliminary Evaluation of the HECM Reverse Mortgage Program

This paper describes and evaluates the Home Equity Conversion Mortgage (HECM) insurance demonstration, designed to encourage the development of private reverse mortgage programs by insuring lenders against the risks associated with new mortgage lending programs and with reverse mortgages in particular. The paper evaluates demand for the program by analyzing the attributes of participating borrowers, their properties and the types of payment options chosen. It also presents several observations regarding participation by the financial community in the HECM demonstration, required counseling and legal and regulatory issues that may hamper the growth and development of reverse mortgage programs in general.
The findings suggest strong demand for reverse mortgages among "house-rich, cash-poor" elderly homeowners, either to supplement inadequate current incomes or to provide a reserve against unexpected lump-sum expenses. The flexible design of the HECM program addresses a wide variety of borrower financial needs, even though it imposes higher costs on lenders and servicers. The continued growth of the program, however, is hindered by a shortage of qualified housing counselors in some areas, as well as by a variety of legal and regulatory barriers.     

Self-Selection in the Fixed-Rate Mortgage Market

This paper analyzes the effect of information asymmetry between the lender and the borrower (i.e., the borrower knows how long he will reside in his home, whereas the lender does not) on the borrower's choice among the interest rate-discount points combinations available in the fixed-rate mortgage market. The analysis shows that if the rate-points trade-off of the mortgage menu is either too steep or too flat, then all types of borrowers will choose the same loan contract from the menu. In addition, if the rate-points trade-off is not convex to the origin, then only the contracts with extreme rate-points combinations will be chosen by borrowers; all contracts with intermediate rate-points combinations are redundant and will not be chosen by any borrowers. Intermediate rate-points combination mortgage contracts would be chosen by some borrowers only if the mortgage menu were to provide a self-selection function. Several necessary conditions of a self-selection mortgage menu are depicted.     

FHA Terminations: A Prelude to Rational Mortgage Pricing

Recent models of pricing mortgages and/or mortgage insurance have used option-pricing models as their framework. The focus is usually on default, which is viewed as a put option (to sell the house to the lender in exchange for the mortgage) and prepayment, which is viewed as a call option (to buy the mortgage from the lender). Analysis then uses techniques like those used to price options in capital markets. Unfortunately, homeowners do not seem to exercise their option as quickly as do traders in organized markets. We estimate prepayment and default functions, which are meant to be a first step in developing modified, option-based models of mortgage pricing.     

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.     

How Subprime Borrowers and Mortgage Brokers Shared the Pie

We develop an equilibrium model for origination fees charged by mortgage brokers and show how the equilibrium fee distribution depends on borrowers' valuation for their loans and their information about fees. We use noncrossing quantile regressions and data from a large subprime lender to estimate conditional fee distributions. Given the fee distribution, we identify the distributions of borrower valuations and informedness. The level of informedness is higher for larger loans and in better educated neighborhoods. We quantify the fraction of the surplus from the mortgage that goes to the broker, and how it decreases as the borrower becomes more informed.     

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.     

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.     

A Closed-Form,After-Tax,Net Present Value Solution to the Mortgage Refinancing Decision

Refinancing one's mortgage is often an attractive, wealth-enhancing option for homeowners in a declining mortgage rate environment. In some respects the decision is simple to analyze because future cash flows are relatively easy to define for fixed-rate mortgages. In other respects, however, the decision is nuanced by option pricing and tax considerations. The analysis must first begin with accurate after-tax, net present value solutions for varying potential holding periods. This study improves upon previous studies, which either ignore tax implications or address them iteratively in spreadsheet model solutions, by introducing a closed-form model that incorporates the ever-changing tax shield of the interest portion of each mortgage payment. Further, unlike many previous studies, our model does not assume that the current and replacement mortgages have equal remaining terms.