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.     

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.     

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.     

The Adjustable Balance Mortgage: Reducing the Value of the Put

We propose a new mortgage contract that endogenously captures the risk of house price declines to minimize default risk resulting from changes in the underlying asset value while still retaining contract rates near the cost of a standard fixed‐rate mortgage. By reducing the role of the legal system in mitigating house price risk, the new mortgage reduces the negative externalities and social costs arising from defaults. In other words, the new mortgage minimizes the need to use the legal foreclosure system to deal with the economic risk of house price declines.     

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.     

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.     

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.     

Optimal Interest Rate-Discount Points Combination: Strategy for Mortgage Contract Terms

This paper is distinguished from previous papers by its focus on income-producing properties, rather than owner-occupied single-family residential properties. The real estate investor's strategy, in terms of choosing an interest rate-discount points combination, is analyzed by using a discounted cash flow approach. Under this framework, the investor with a lower marginal tax rate, lower required rate of return and longer investment horizon tends to negotiate for a mortgage contract with a higher number of discount points and lower interest rate. In addition, an intermediate rate-points combination is preferred by an investor only when the lender's required interest rate is a decreasing convex function of the number of discount points.     

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.     

Mortgage Pricing: Some Provisional Empirical Results

We test some of the qualitative properties of mortgage pricing models. The models use option pricing techniques, focusing on prepayment as a call option. They imply a quite nonlinear relationship between mortgage price and coupon, interest rates and volatility. We test for both the first and second derivatives of the effects of these variables using data on Ginnie Mae mortgage backed securities. We find that the model is largely supported by the data.     

The Demand and Supply of Mortgage Funds and Mortgage Loan Terms

The supply of and demand for residential mortgages has been the subject of much discussion in the literature. Many of these studies have used single equation, partial adjustment models with the price specified as the contract rate. In this study, two of the assumptions that underlie these previous studies are tested empirically. First, the proper specification of the price of mortgage funds is tested by using both the contract rate alone and all of the terms of the mortgage as the price. Second, the speed of adjustment in the mortgage market is examined by estimating the model in both the instantaneous adjustment and partial adjustment forms. Both of these tests are carried out using a simultaneous equation rather than a single equation model. The empirical results indicate that the contract rate along with the loan initiation fees, the loan-to-value ratio and the maturity is the better specification of price and that the partial adjustment model performs better than the instantaneous model in the mortgage market.     

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.     

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.     

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.     

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.     

Mortgage Insurance Adoption in the Netherlands

Individuals tend to underinsure on low probability, high consequence risks. Using a survey data set from a unique institutional context, we provide an assessment of the underinsurance puzzle by studying mortgage insurance adoption among Dutch homeowners. The results indicate that the demand for mortgage insurance is affected by risk exposure, type of mortgage lender, and the involvement of financial advisors. We document that wealthier and younger mortgagors are more likely to insure. However, locus of control, house price expectations, and precautionary savings are not related to insurance demand. Finally, we find evidence that borrower (over)confidence negatively affects the likelihood that insurance is bought.     

浅析利率调整对住房抵押贷款违约风险的影响

住房贷款利率的变化对房地产价格产生着巨大影响，房地产价格又是住房抵押贷款中重要因素，与住房抵押贷款风险密切相关。违约风险是住房低押贷款风险中最基本最主要的风险，也称信用风险。论文将从理论上分析利率政策调整对住宅抵押贷款违约风险的影响，并提出相应的防范措施。     

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.     

Reversing the Trend: The Recent Expansion of the Reverse Mortgage Market

Reverse mortgages allow elderly homeowners to tap into their housing wealth without having to sell or move out of their homes. However, very few eligible homeowners used reverse mortgages to achieve consumption smoothing until recently, when the reverse mortgage market in the United States witnessed substantial growth. In this article, I examine 1989–2007 loan‐level reverse mortgage data and conduct three sets of analyses to better understand the demand for reverse mortgages among elderly homeowners. First, I study the ZIP code characteristics correlated with reverse mortgage originations. Second, I show that recent reverse mortgage borrowers are significantly different from earlier borrowers in many respects. Third, I investigate the reasons why the reverse mortgage market experienced substantial growth in the mid‐2000s. Combining the reverse mortgage data with county‐level house price data, I find that higher house prices lead to more reverse mortgage originations. Specifically, the increases in house prices account for about one‐third of the overall growth in the reverse mortgage market from 2003 to 2007.     

The Borrower's Perceived Risk in Mortgage Choice

We investigate how borrowers perceive the risk in the adjustable rate mortgage (ARM) versus fixed rate mortgage (FRM) choice. We develop a mortgage choice model where the coefficient on the long‐term bond risk premium is conditional on the borrower's perceived risk. We show that the perceived risk fluctuates over time according to the short‐term interest rate level and housing market conditions. We find that when the short‐term rate level is high (low), the borrowers perceive low (high) risk of a short‐term rate rise, thus opting for ARMs (FRMs). Also, during a down housing market they become more risk‐averse perceiving higher risk in choosing ARMs. The perceived risk level alters the borrowers’ sensitivity to the long‐term bond risk premium.