Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages

This paper integrates two fundamentally important parameters into a theory of optimal mortgage design: the proportion of inflation risk borne by the lender / investor and the borrower and the amortization-graduation schedule for loan repayments. Equations are derived for a family of innovative mortgages, termed hybrid PLAMs, which offer advantages to borrowers and lenders over either the standard fixed rate mortgage (FRM) or the price level adjusted mortgage (PLAM). The superiority of the hybrid PLAMs lies in their ability to simultaneously and independently accommodate differing degrees of inflation-risk sharing and payment affordability. Inflation-risk sharing is represented by an indexation parameter set over a continuum of values such that the FRM has zero index variability and the PLAM has unit index variability. Similarly, payment tilt is represented by a tilt parameter such that the FRM has zero tilt and the PLAM has unit tilt. We demonstrate that these two parameters are independent and can each be continuously varied in a two-dimensional family of self-amortizing mortgages. A specific hybrid PLAM can be designed to partition inflation risk in any proportion between the borrower and the lender and to simultaneously prescribe any level of payment tilt between the extremes of the FRM and PLAM. The behavior of representative hybrid PLAMs is simulated and compared to FRMs and PLAMs for three different inflation scenarios, one of which uses actual market data from the period of 1960–1990.     

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.     

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.     

The Termination of Subprime Hybrid and Fixed‐Rate Mortgages

Adjustable‐rate and hybrid loans have been a larger component of subprime mortgage lending in the mortgage market than prime lending. The typical adjustable‐rate loan in subprime is a hybrid of fixed and adjustable characteristics in which the first 2 years are fixed and the remaining 28 years adjustable. Hybrid loans terminate at elevated probabilities even before the first adjustment date. Hybrid loan terminations are sensitive to interest rates and teaser rates (payment shocks). Default probabilities increase dramatically when payment shocks are mixed with low or no equity in the home. This is the mixture of events that helped to trigger the 2007/2008 subprime mortgage crisis.     

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.     

The Flexible Mortgage: Optimal Financing of a Consumer Durable

Given the recent flood of new mortgage innovations, it is natural to wonder what features a mortgage which is "optimal" from the consumer's point of view might possess. This paper investigates this issue, using optimal control theory to characterize the time profile of mortgage payments (as well as the value of the mortgage) that maximizes an intertemporal utility function. Among other things, the analysis shows that the optimal mortgage payment stream rises over time under reasonable assumptions, highlighting the non-optimality of the standard flat-payment mortgage.     

Do Riskier Borrowers Borrow More?

Conventional wisdom in the mortgage industry holds that loan-to-value (LTV) ratios are positively correlated with mortgage default rates. However, not all empirical studies of mortgage loan performance support this view. This paper offers a theoretical signaling model of why the correlation between LTV ratios and default risk is contingent upon the default costs of the borrower. Specifically, the model proposes that when default costs are high there exists a separating equilibrium in which risky borrowers will self-select into lower LTV loans to reduce the probability of facing a costly default, while safe borrowers will self-select into higher LTV loans as a signal of their enhanced creditworthiness. This adverse selection process gives rise to the possibility of higher default probabilities for lower LTV loans. Conversely, when default costs are low the conventional result, in which risky borrowers select higher LTV loans than safe borrowers, is obtained. Empirical results, based on a sample of 859 single-family residential mortgage loans drawn from the portfolio of a national mortgage lender, are consistent with the separating equilibria predicted by the model.     

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.     

Short-term financing in a cash-constrained supply chain

In this paper we consider a two-level supply chain with a single retailer and a manufacturer, where both the firms are facing financial constraints and can not produce/order their optimal quantity. Our work shows that a lender who finances the manufacturer has a motivation to finance the retailer as well. Motivated by this, we investigate lender's problem of financing both the firms by making a joint decision on the loan amount and comparing it with the case when lender makes independent decision on loan amount for both the firms. Our numerical study indicates that if one of the firms in the supply chain has sufficiently low cash, joint decision (we refer to it as supply chain financing) may be better not only for the lender but for the retailer and manufacturer as well.     

The Effect of Mortgage Payment Reduction on Default: Evidence from the Home Affordable Refinance Program

This article evaluates the effect of payment reduction on mortgage default within the context of the Home Affordable Refinance Program. We find that mortgage default is sensitive to payment reduction using univariate, duration and hazard modeling approaches. A relative risk Cox model of default with time‐varying covariates estimates that a 10% reduction in mortgage payment is associated with about a 10–11% reduction in monthly default hazard for loans. This finding is robust to the inclusion of empirically important mortgage risk drivers (such as current loan‐to‐value and FICO score) as well as controlling for selection effects based on observables.     

Down Payment Saving in the United States: Evidence from the Panel Study of Income Dynamics

We present a model of household saving toward a mortgage loan under an exogenous down payment requirement and preference for owning over renting. Our model explains a set of empirical observations such as the dual effect in the form of some households, in response to higher down payments, becoming discouraged savers while those who do not abandon purchasing plans save more. We also employ instrumental variable‐based methods to investigate the down payment saving behavior of first‐time home buyers in the United States. The empirical results based on Panel Study of Income Dynamics (PSID) data support the inelastic down payment elasticity of saving implied by our model.     

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.     

住房抵押贷款提前还贷风险管理研究

从现代金融和风险管理角度看,住房抵押贷款提前还贷对商业银行是一种期权性风险,对其收取违约金并非国际惯例,也并不是有效的风险补偿方式。商业银行应适应市场竞争需要,接受风险转嫁并提供风险管理服务,运用风险定价技术在按揭交易价格中对提前还贷风险进行补偿。对于已承担的风险,商业银行应构建抵押贷款提前还贷的数据库,通过表内对;中和市场对冲,推出多样化的住房抵押贷款方式,积极推进住房抵押贷款证券化．从而最终增强银行的盈利来源和核心竞争力。     

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.     

建立住房抵押贷款保险制度促进房地产市场的发展

文章针对目前国内个人住房消费的现状,对现行的 押贷款体系中存在的问题进行了分析丐研究,提出了相应的对策,即建立住房抵押贷款保险制度。借鉴国际上发达国家的做法,通过保险分散抵押代款的风险,完善社会保障体系,促进个人住房抵押贷款的良性发展,进而房地产市场的健康发展。     

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.     

Residential-Mortgage Lending Discrimination and Lender-Risk-Compensating Policies

The Boston Federal Reserve study ( Munnell et al. 1996 ) concluded that illegal discrimination is a statistically significant contributor to the observed gap between white and minority residential-mortgage rejection rates. The Boston study speculated that discrimination arises because lenders do not equally apply risk compensation or mitigation policies for imperfect loans. Using the same 1990 Boston loan application data, our study specifically examines the relation between compensating policies and discrimination. Since compensating policies are encouraged by secondary-mortgage-market sale guidelines, we model both the lender's origination decision and its loan sale decision. Using a rule-based artificial-intelligence technique applied to each lender, we infer compensating policies (rules) that equally apply to all races and explain lending decisions. A minority-race indicator loses its statistical significance when an indicator of compensating-policy violations appears in the loan accept–reject equation. This result reflects the fact that the risk levels of marginal minority loans tend to be more extreme than those of marginal white loans. However, the result does not necessarily reject the existence of discrimination. Equally applied policies may be empirically indistinguishable from unfairly applied policies. In addition, equally applied policies may fail the adverse-impact doctrine if they do not serve a business necessity (such as profits). The industry's move away from discretionary, rule-based decisions to mortgage scoring answers the need for a decision framework that rigorously uses loan performance to evaluate all loan applicants fairly.     

A Note on Identification of Discrimination in Mortgage Lending

This paper shows how reduced form estimates of discrimination in mortgage lending may be biased by race differences in loan demand. The result, which follows formally from the model of the mortgage lending process developed in the seminal paper by Maddala and Trost (1982), has important implications for the regulation of financial institutions. It also reinforces findings of Rachlis and Yezer (1993) and Yezer, Phillips and Trost (1994). A review of recent empirical evidence on race differences in loan demand suggests that this factor may help explain mortgage loan application differentials.     

The Termination of Commercial Mortgage Contracts through Prepayment and Default: A Proportional Hazard Approach with Competing Risks

This article examines the factors driving the borrower's decision to terminate commercial mortgage contracts with the lender through either prepayment or default. Using loan–level data, we estimate prepayment and default functions in a proportional hazard framework with competing risks, allowing us to account for unobserved heterogeneity. Under a strict definition of mortgage default, we do not find evidence to support the existence of unobserved heterogeneity. However, when the definition of mortgage default is relaxed, we do find some evidence of two distinctive borrower groups. Our results suggest that the values of implicit put and call options drive default and prepayment actions in a nonlinear and interactive fashion. Prepayment and default risks are found to be convex in the intrinsic value of call and put options, respectively. Consistent with the joint nature of the two underlying options, high value of the put/call option is found to significantly reduce the call/put risk since the borrower forfeits both options by exercising one. Variables that proxy for cash flow and credit conditions as well as ex post bargaining powers are also found to have significant influence upon the borrower's mortgage termination decision.     

Contemporaneous Loan Stress and Termination Risk in the CMBS Pool: How “Ruthless” is Default?

This study analyzes the impact of contemporaneous loan stress on the termination of loans in the commercial mortgage‐backed securities pool from 1992 to 2004 using a novel measure, based on changes in net operating incomes and property values at the metropolitan statistical area‐property‐type‐year level. Employing a semi‐parametric competing risks model for a variety of specifications, we find that the probability of default is extremely low even at very high levels of stress, although the coefficient estimates of greatest interest are very statistically significant. These results suggest substantial lender forbearance and are consistent with previous research that models default as a “gradual dynamic process” rather than a “ruthless” exercise once “in the money.”