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.     

Credit Rationing and Government Loan Programs: A Welfare Analysis

Asymmetric information about borrower default probabilities may lead to inefficient credit rationing of low-risk borrowers in otherwise competitive markets. In a simple model having these properties, we show that some types of government loan programs, such as loan guarantees issued through lenders, might improve economic efficiency. But the incentive for high-risk borrowers to misrepresent their loan quality is worsened by other government loan programs, notably those that try to target aid directly to rationed borrowers. As such, cost-effective programs may increase inefficiency. This surprising result highlights the need to conduct model-specific policy analyses, as opposed to analyses based on model-free performance indicators.     

A Note on Equivalent Fixed Rate and Variable Rate Loans; Borrower's Perspective

A common situation is where a borrower is offered the choice of two types of loans—a fixed interest rate loan for a fixed period or a variable interest (floating interest) rate loan. Usual wisdom and advice is that the borrower opts for the fixed rate loan if interest rates are anticipated to rise in the future or opts for the variable rate loan if interest rates are anticipated to fall. However, depending on the magnitude of the rates offered, and the rate uncertainty in the market, such wisdom may not always be well founded. This note demonstrates why this might be. It derives a readily usable, low-mathematical-background expression showing, for borrowers, when fixed and variable rate loans are equivalent and when one rate type is better/worse than the other.     

Lenders’ pricing strategy: Do neighborhood risks matter?

This article explores the different pricing strategies of lenders who originate both government-sponsored enterprise (GSE) and non-GSE loans. We find that conditional on loan and borrower characteristics and some observable local economic factors, mortgage rates on GSE loans vary significantly across regions. However, we observe no sizable regional variation in loan amounts or default risk. By contrast, the mortgage rates on non-GSE loans depend almost entirely on borrowers and loan characteristics. In addition, we find that spatial variations in GSE mortgage rates are highly responsive to regional prepayment risk. Our results are robust to various controls for neighborhood characteristics, including regional-level bank competition, borrower accessibility to mortgages, and household income levels. Overall, the findings offer a novel insight into how lenders adjust pricing strategies in response to a changing lending environment. The results provide implications relating to the present and imminent dangers of housing bubbles and the intensified refinancing wave following the COVID-19 pandemic.     

The Effect of Refinancing Costs and Market Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts

This article, which was originally written in 1986, develops a methodology for valuing mortgage-backed securities with refinancing costs. We solve simultaneously for the valuation of the mortgage-backed security (loan) and the borrower's refinancing strategy, pricing all coupon levels simultaneously. Because the borrower may refinance his or her loan and incur costs at many times in the future, the optimal refinancing decisions arise from an optimal dynamic strategy that reflects the costs of all potential future refinancings. Though the borrower faces multiple rounds of refinancing costs, the market value of the loan cannot exceed the call price plus a single round of refinancing costs.     

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.     

Stochastic Modeling of Federal Housing Administration Home Equity Conversion Mortgages with Low-Cost Refinancing

Federal Housing Administration-insured reverse mortgages, known as Home Equity Conversion Mortgages (HECMs), did not originally have a provision for low-cost refinancing. If a borrower's house value increased faster than expected, the borrower could not tap that additional equity without terminating the first loan and originating a new HECM loan with full closing costs. We test several low-cost refinancing options using a stochastic simulation model that allows interest rates and house prices to vary in historically accurate patterns. Low-cost refinancing decreases the net value of the fund by 54% to $98.5 million, but it remains positive in 80% of the trials.     

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.     

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.     

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.     

Explaining Refinancing Decisions Using Microdata

This paper develops a model which explains how mortgage-rate movements, transactions costs, changes in borrower income and house value, personal financial opportunities and the prepayment option embedded in fixed-rate mortgages affect a financially flexible borrower's decision to refinance an existing loan while retaining the underlying home. Broadening the focus of previous analytical work, the model explains why households with similar mortgage loans may react differently as financial market conditions change. It contains definitive empirical predictions that are supported by an analysis of a choice-based sample of individual loan transactions. Results suggest that refinancings are motivated both by movements in the level of interest rates and by borrowers' desires to alter their capital structures in the face of changing income and housing wealth.     

Valuing the Defeasance Option in Securitized Commercial Mortgages

To protect the interests of investors, commercial mortgage loans pooled for the issuance of commercial mortgage-backed securities (CMBS) have restrictive covenants that discourage the borrower from refinancing. Such restrictions limit the borrower's ability to access any accumulated equity. The predominant means of accessing this equity today is defeasance. By defeasing a loan, the borrower substitutes the commercial mortgage with U.S. Treasury or agency obligations whose payments match those of the defeased mortgage. Therefore, defeasance is an exchange option whereby the borrower gives up the portfolio of Treasury or agency securities and in return receives the market value of the commercial mortgage plus the liquidity benefits arising from accessing the accumulated equity in the underlying property. The value of the option to defease is shown to depend critically on the rate of return that can be earned on the released equity, prevailing interest rate conditions, as well as the option's contractual features.     

Search Frictions in Many-to-one Markets*

This article studies how search frictions affect competition and matching efficiency in many-to-one loan markets where a borrower requires support from multiple investors and coordination is desired but absent. We develop a dynamic search model and show that borrowers employ mixed strategies in quoting interest rates. More importantly, we find that in many-to-one markets, the rate dispersion caused by search frictions facilitates coordination and hence improves allocation efficiency relative to a no friction environment. Further, we empirically present stylized facts consistent with the theoretical predictions and structurally estimate the impact of search frictions on matching efficiency.     

Price Premium and Foreclosure Risk

Many previous studies identify loan, property, borrower and environmental factors that impact the probability of foreclosure. Implicit in these studies is the assumption that the property was purchased at fair value. We question this assumption based on several empirical findings regarding property value uncertainty. In contrast to previous research, we explicitly quantify the price premium from a hedonic pricing model. Using a comprehensive database of real estate transactions in Singapore during 1989–2000, we document a price premium associated with properties that are subsequently foreclosed based on actual sales transactions. In addition, we find that the premium paid at purchase significantly increases the probability of foreclosure. These results are robust and continue to hold after controlling for other property-specific factors, time-varying macroeconomic conditions, alternative model specifications and definitions of price premium.     

The HAMP NPV Model: Development and Early Performance

The foreclosure crisis that began in 2008 triggered the need for new approaches to treat distressed mortgages. A key component of the Obama Administration's Home Affordable Modification Program (HAMP) was the development of a standardized Net Present Value (NPV) Model to identify troubled loans that were value‐enhancing candidates for payment‐reducing modifications. This article discusses the development of the HAMP NPV Model, 1 its purpose and some important constraints that dictated its structure and limitations. We describe the structure and the estimation of the model in detail. We also describe the responsiveness of the model to key characteristics, such as loan‐to‐value and credit score, as well as provide new evidence on the relationship between HAMP modification performance and key borrower and modification characteristics. The article concludes with a discussion of model limitations and the future role of systematic loan modification using NPV analysis.     

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.     

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.     

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.     

The Effects of Securitization on Consumer Mortgage Costs

We examine the effects of securitization on two dimensions of consumer mortgage costs: coupon rates and loan origination fees. We find no evidence that securitization reduces the coupon rates on fixed- or adjustable-rate mortgages. Instead, securitization appears to lower mortgage loan origination fees, resulting in substantial savings for consumers. Securitization activity includes passthrough creation and collateralized mortgage obligation (CMO) creation. We test for differences between the effects of passthrough and CMO creation on primary mortgage costs. Surprisingly, these activities appear to have indistinguishable effects on loan rates and origination fees, suggesting that a large derivatives market for mortgage loans is not creating value for consumers.     

Modelling reverse mortgages

This paper suggests a framework for analyzing reverse mortgages in a fixed interest rate environment as well as a variable interest rate environment. To analyze the risk and potential profit of a reverse mortgage, we propose to calculate the expected present value of profit and the probability of loss as indicators of the viability of the loan. Using Singapore data, we provide some estimates of these quantities for various levels of annuity payment under different circumstances.The author is from the Department of Economics and Statistics, National University of Singapore. He wishes to thank Chan Wai Sum, Thomas Herzog, Lim Kian Guan (the previous chief editor), Tan Kin Lian and Albert Tsui for their invaluable comments on the earlier drafts of the paper. All errors and shortcomings, however, remain his responsibility.