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.     

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.     

Handing Over the Keys: A Perspective on Mortgage Default Research

This paper is the text of the 1992 Presidential Address for the American Real Estate and Urban Economics Association. A comparative evaluation of mortgage default research finds that both the residential and commercial markets evolved from informal underwriting rules, to formalized (though unvalidated) ratios and rules of thumb, to early risk ratings based upon empirical evidence, to gener-alizable econometric models of default, to option-based pricing models. The commercial market lagged the residential market by about 10 to 20 years at first but is now only about five years behind. The survey finds that research and progress in understanding mortgage credit risk has been precipitated by a public policy need or mandate, data availability, and adequate technology. The absence of any one of these factors has hindered progress in the past. Finally, six emerging issues in default research are identified and discussed: (1) the degree of "ruth-lessness" with which default is exercised, (2) loan recourse, (3) the magnitude and timing of revenues and losses associated with default, (4) loan modification, (5) default in a portfolio context, and (6) leasehold default. Progress in these areas will enhance the efficiency of both the residential and commercial markets.     

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.     

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.     

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.     

Where is the opportunity in opportunity zones?

In December 2017, the U.S. Congress passed into law the Opportunity Zone (OZ) program. As an OZ, designated low-income census tracts provide considerable tax breaks to property investors, intending to attract investments and spur economic growth. As the success of the program is dependent on investors' responses, we analyze market reactions in a difference-in-differences framework. We identify two potential effects on property markets: tax breaks for investors and expected land value appreciation. Our results show that tax breaks are priced efficiently. Qualified properties increase by 7–20% in price, while vacant land increase up to 37%. In contrast, we find limited signs of expected land value appreciation.     

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.     

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.     

The Impact of Interstate Foreclosure Cost Differences and the Value of Mortgages on Default Rates

Previous research on mortgage default has focused on the costs, benefits, and characteristics of the mortgagor. In such studies default rates have been taken as a measure of mortgage risk. In this paper we present a model where the position of the lender affects the default-foreclosure process. Important to the lender's decision to foreclose rather than renegotiate an existing loan are the value of mortgage and the legal costs associated with foreclosure.
The empirical evidence supports the hypothesis that both the value of the mortgage and legal foreclosure costs affect the foreclosure rate. In those states where legal foreclosure costs are high rates are significantly less than where costs are low. This suggests that previous models which include only the costs and benefits of default to the borrower are incomplete and that foreclosure rates can not be taken as a strict measure of mortgage risk. That is, low foreclosure rates may indicate that losses occur in other forms of loan negotiation rather than in expensive legal costs.     

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.     

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.     

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.     

Residential Mortgage Credit Derivatives

As the fallout from subprime losses clearly demonstrates, the credit risk in residential mortgages is large and economically significant. To manage this risk, this article proposes the creation of derivative instruments based on the credit losses of a reference mortgage pool. We argue that these derivatives would enable banks to retain whole loans while also enjoying the capital benefits of hedging the credit risk in their mortgage portfolios. In comparisons of hedging effectiveness, the analysis shows that instruments based on credit losses outperform contracts based on house price appreciation.     

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.     

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.     

Thy Neighbor’s Mortgage: Does Living in a Subprime Neighborhood Affect One’s Probability of Default?

This article focuses on the potential externalities associated with subprime mortgage origination activity. Specifically, we examine whether negative spillover effects from subprime mortgage originations result in higher default rates in the surrounding area. Our empirical analysis controls for loan characteristics, house price changes and alternative loan products. Our results indicate that, after controlling for these characteristics, the concentration of subprime lending in a neighborhood does not lead to greater default risks for surrounding borrowers. However, we do find that more aggressive mortgage products (such as hybrid adjustable rate mortgages and low/no‐documentation loans) had significant negative spillovers on other borrowers. Stated differently, the aggressive alternative mortgage designs were more toxic to the housing and mortgage market than previously believed.     

Commercial Mortgage Defaults: Proportional Hazards Estimation Using Individual Loan Histories

This paper examines the theory of commercial mortgage default and tests it using a data set of 2,899 loan histories provided by a major multi-line insurance company. A default model is estimated which relates subsequent default incidence and timing to contemporaneous loan term, borrower, property and economic/market conditions. Maximum likelihood estimation is used to estimate a hazard function predicting conditional probability of default over time. Results confirm many expected default relationships, in particular the dominance of loan terms and property value trends over time in affecting default. The effectiveness of the model in discriminating between "good" and "bad" loans is explored. Implications for underwriting practice and credit risk diversification are noted. Finally, suggestions are made for extending these results in pricing applications.     

Equity Dilution: An Alternative Perspective on Mortgage Default

Empirical research on mortgage default in the single-family market has focused on the value of the borrower's put option using house price indices to estimate contemporaneous loan-to-value ratio or the probability of negative equity. But since the borrower possesses the option to increase leverage by taking on additional debt secured by junior liens subsequent to loan origination (a phenomenon termed here equity dilution ), even a perfect house price adjustment cannot be expected to accurately measure changes in borrower equity over time. Since junior liens are generally unobservable to senior debt holders, proxies are required in empirical applications. This paper employs an independent estimate of junior lien probability developed from the 1998 Survey of Consumer Finances combined with loan level mortgage performance data to examine the role junior liens play in increasing default risk.     

Expected and Actual Effects of Housing Allowances on Housing Prices

Most analysts and policy makers expected fullscale housing allowance programs to substantially disturb local housing markets, causing housing prices tb increase sharply. This paper reviews conjectures about expected price effects, summarizes evidence from the Housing Assistance Supply Experiment, and explains why the program did not engender the expected price inflation.