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.     

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.     

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.     

Housing Finance in a Stochastic Economy: Contract Pricing and Choice

An empirical analysis of macroeconomic time series from the mortgage, housing, capital and labor markets is based on life-cycle consumption and mortgage option pricing considerations. Vector autoregression techniques characterize the long-run equilibrium and short-run dynamics of the mortgage market as it relates to the other sectoral markets. A simultaneous-equations model characterizes the partial equilibrium in the differentiated products market for fixed- and adjustablerate mortgage contracts. The empirical results reveal the impacts that market conditions have on mortgage volumes and prices, and they generally support the implications of the consumption and pricing theories.     

Pricing Mortgage-Backed Securities: Integrating Optimal Call and Empirical Models of Prepayment

Residential mortgage borrowers frequently appear to behave suboptimally with respect to their mortgage prepayment options. Many borrowers fail to exercise even well-into-the-money options while others prepay when the call option is out-of-the-money. To account for these apparently suboptimal prepayments, the recent trend in mortgage-backed securities research has been away from optimal call valuation models, in which the decision to exercise is determined endoge-nously, in favor of models in which prepayment behavior is exogenously specified based on empirical estimation. This paper develops a rational model of mortgage prepayment which incorporates both types of "non-optimal" prepayment and retains endogenous call. This enables the model to disentangle and compare the separate effects of the interest rate call, impeded by transaction costs, and of non-interest-rate driven prepayment. In addition, by recognizing heterogenous borrower transaction costs, the model presents a way to account more precisely for the varying prepayment lags associated with well-into-the-money call options and to account for the phenomenon of "burnout" within a mortgage pool. The paper includes an empirical test of the unbiasedness of the integrated pricing model by comparing simulated prices from our theoretical model to observed prices on traded Fannie Mae and GNMA securities.     

Hedging Forward Mortgage Loan Commitments: The Option of Futures and a Future for Options

The purpose of this paper is to analyze theoretically the problem of how mortgage lending institutions assume the interest rate risks inherent in the granting of fixed-rate mortgage loan commitments.
Two approaches to hedge this risk are analyzed. First, the use of the GNMA futures market is evaluated from the standpoint of how it might be used to hedge against mortgage commitment risks. Secondly, the use of an appropriate pricing model—the Black-Scholes option pricing model—is offered as a proxy for establishing the market value of a fixed-rate mortgage commitment. This model is extended and empirically estimated for several hypothetical environments.
The paper demonstrates a basic flaw in the GNMA futures market as a hedge against mortgage commitments. Once this is established, the use of the options pricing approach is offered as a more rational approach for hedging these risks.     

Efficiency in the Mortgage Market: The Borrower's Perspective

This paper uses mortgage history data from the Federal Home Loan Mortgage Corporation to analyze the prepayment behavior of homeowners and to test whether borrowers exercise their prepayment options in a manner consistent with contingent claims models. A variety of hazard models are estimated from individual data on more than 6000 mortgages issued during the 1976–1980 period. In these models, it is clear that the extent to which the prepayment option is "in the money" has a strong effect on behavior. However, it is less clear that the option is exercised quite as ruthlessly as the theory predicts.     

Information Externalities,Neighborhood Characteristics and Home Mortgage Pricing and Underwriting

Theories of rational redlining suggest thinness in housing markets should lead to greater uncertainty in house price appraisals, increasing mortgage denial rates or pricing. Empirical tests found support for this theory in mortgage underwriting using 1990s data. Using 2006 data and bank‐specific regression models, we revisit this topic in light of two developments leading to the recent mortgage bubble: the widespread securitization that allowed banks to shift loan risk to investors and the advent of risk‐based pricing. Consistent with expectations, we find that information externalities have become economically very small and have shifted from underwriting to pricing decisions.     

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.     

Choice of Mortgage Contracts: Evidence from the Survey of Consumer Finances

This study revisits the empirical question of the determinants of the choice between fixed‐ and adjustable‐rate mortgages using data from the Survey of Consumer Finances that overcome some of the data limitations in previous studies. The results from a logit model of mortgage choice indicate that pricing variables and affordability are important considerations. We also find that factors, such as mobility expectations, income volatility and attitudes toward financial risk largely influence mortgage choice, with more risk‐averse borrowers preferring fixed‐rate mortgages. For households that are less risk averse, the mortgage type choice decision is less sensitive to pricing variables and income volatility, and affordability factors are not significant. These findings provide empirical support that underscores the importance of attitudes toward risks in mortgage choice.     

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.     

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.     

Contracts as Options: Some Evidence from Condominium Developments

This paper values the real estate option to purchase contract in a contingent claims framework. The model is an application of the Black and Scholes option pricing model. Observed market data on the sale of condominiums are used to test if the option is competitively priced under various assumptions regarding the expected instantaneous variance of the condominium price. Simulation results suggest that standard industry practices of charging a fixed amount for the option to purchase roughly conform to pricing behavior dictated by the option pricing model.     

Differential Access to and Pricing of Home Mortgages: 2004 through 2009

This article documents trends and drivers of the residential mortgage market during the years 2004 through 2009, specifically focusing on the access to and pricing of mortgages originated by African‐American and Hispanic borrowers, and by borrowers living in low‐income and minority communities. Our analysis relies on a rich set of proprietary data that allow more expanded insights than can be obtained from the Home Mortgage Disclosure Act (HMDA) alone. We show that access to mortgage credit increased between 2004 and 2006 for the borrowers we focus on in our study and declined dramatically thereafter. Trends in access to credit were driven primarily by the changing credit mix of mortgage applicants and secondarily by the replacement of the Federal Housing Administration (FHA) for subprime as the dominant mode of nonprime originations and tighter underwriting standards. Throughout our entire period of study, these borrowers also consistently paid higher prices for their mortgages; however, the extent of this differential varied considerably over time and across groups. These pricing trends were driven primarily by changes in the FHA and subprime shares as well as by the market's increasingly aggressive pricing of credit risk.     

Mortgage Brokers,Origination Fees,Price Transparency and Competition

This article examines the dynamics between mortgage broker competition, origination fees and price transparency. A reverse first‐price sealed‐bid auction model is used to motivate broker pricing behavior. Confirming the model predictions, our empirical analysis shows that increased mortgage brokerage competition at the Metropolitan Statistical Area level leads to lower fees. The findings are robust to different measures of fees as well as different measures of competition. We also provide evidence that broker competition reduces mortgage origination fees on retail (nonbrokered) loans as well. In addition, our results indicate that pricing complexity is an important determinant of fees, and increased broker competition is associated with a higher probability of a loan being priced with transparency. Our results suggest that mortgage brokers increase competition and lower fees in the mortgage market.     

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.     

Commercial Office Space: Testing the Implications of Real Options Models with Competitive Interactions

We test the implications of real option pricing models with competitive interactions for commercial real estate development. The competitive nature of a local commercial real estate market relies on a Herfindahl ratio derived from individual developers' shares of total office construction in their market. All else being equal, greater competition among local developers is associated with more building starts. Other variables suggested by the real options pricing model, including the volatility of local lease rates, are also found to be statistically important. In addition, we provide evidence consistent with greater competition attenuating the extent to which increases in volatility delay commercial real estate development.     

Pricing Private Mortgage Insurance

Issues involved in an evaluation of the price of private mortgage insurance are discussed. Cost considerations are emphasized as long-run equilibrium competitive market prices equal long-run marginal and average cost. An empirical evaluation of current insurance premiums vis-a-vis competitive market norms requires more empirical information on the determinants of foreclosures, especially the links between micro and macro determinants. Option pricing models suggest other data comparisons that also may shed light on an evaluation of insurance premiums.     

Price Dispersion in Mortgage Markets

Using transaction‐level data on Canadian mortgage contracts, we document an increase in the average discount negotiated off the posted price and in rate dispersion. Our aim is to identify the beneficiaries of discounting and to test whether dispersion is caused by price discrimination. The standard explanation for dispersion in credit markets is risk‐based pricing. Our contracts are guaranteed by government‐backed insurance, so risk cannot be the main factor. We find that lenders set prices that reflect consumer bargaining leverage, not just costs. The presence of dispersion implies a lack of competition, but our results show this to be consumer specific.