House‐Price Expectations,Alternative Mortgage Products,and Default

The goal of this paper is to better understand the forces that spurred use of alternative mortgages during the housing boom. A theoretical model shows that, when future house‐price expectations become more favorable, reducing default concerns, mortgage choices shift toward alternative products, which are characterized by backloading of payments. The empirical work confirms this prediction by showing that an increase in past house‐price appreciation, which captures more favorable expectations for the future, raises the market share of alternative mortgages. In addition, the paper tests the fundamental presumption that backloaded mortgages are more likely to default, finding support for this view.     

Mortgage Choice in the Euro Area: Macroeconomic Determinants and the Effect of Monetary Policy on Debt Burdens

This paper provides novel evidence on the role of the macroeconomic environment for households’ choice between fixed‐interest‐rate and adjustable‐interest‐rate mortgages (ARMs) in the euro area. We find that relatively more ARMs are taken out when economic growth is strong, the interest rate spread is high, or unemployment shows low volatility. A simulation exercise shows that a reduction in mortgage rates as witnessed during the monetary easing in the course of the global financial crisis produces a substantial decline in debt burdens among mortgage‐holding households, especially in countries where households have higher debt burdens and a larger share of ARMs.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

Appraisal Quality and Residential Mortgage Default: Evidence from Alaska

We empirically examine the effect of appraisal quality on subsequent mortgage loan performance using data from the high volatility housing market of Alaska in the 1980s. We develop measures of appraisal quality by computing the residual between a hedonic estimate of house value using available information from other appraisals compared to actual ex ante appraised value. We then estimate proportional hazard models of mortgage default and find that several measures of appraisal quality, particularly appraised value in excess of hedonic estimates, are significantly related to default risk. Using valuations subsequent to loan default, we are also able to evaluate how well house price indices perform in terms of estimating current loan-to-value and offer some additional evidence on the controversy over the role of net equity versus trigger events as determinants of mortgage default. We also show that defaults are related to ex ante measures of housing market conditions, with additional implications for underwriting policies and the current industry trend away from traditional appraisal and toward automated valuation.     

Mortgage Default with Asymmetric Information

This article analyzes mortgage-market equilibrium when borrower default costs are private information. By applying the approach of Rothschild and Stiglitz (1976), it is shown that asymmetric information regarding default costs distorts the contract choices available in the mortgage market, preventing safe borrowers (those with high default costs) from fully satisfying their demand for mortgage debt. Large loans are available for a substantial interest-rate premium, but only risky borrowers find this premium worth paying. The article builds on an empirical literature designed to test the ruthless-default principle from option-based models of mortgage pricing. That literature provides evidence against ruthless behavior, suggesting that default costs play an important role in borrower decisions. The article takes a further step by arguing that such costs are private information, which has important implications for market equilibrium.     

Embedded Options in the Mortgage Contract

Loss mitigation is the process by which lenders attempt to minimize losses associated with foreclosure. As competition increases in the mortgage industry, lenders and servicers are under great pressure to adopt loss mitigation tactics rather than simply use foreclosure as the means of dealing with borrowers in default. This study presents a mortgage-pricing model that fully specifies all borrower options with respect to default, including the ability to reinstate the mortgage out of default. We document the impact of various loss mitigation programs, including forbearance and antideficiency judgments, as well as the value of credit on borrower default behavior.     

Beyond the Transaction: Banks and Mortgage Default of Low‐Income Homebuyers

We evaluate the effects of the lending institution and soft information on mortgage loan performance for low‐income homebuyers. We find that even after controlling for the propensity of a borrower to get a loan from a local bank based on observable characteristics, those who receive a loan from a local bank branch are significantly less likely to become delinquent or default than other bank or nonbank borrowers, consistent with an unobserved information effect. These effects are most pronounced for loans originated to borrowers with marginal credit, where soft information may have a stronger effect. These findings support previous research on information‐driven lending, and provide additional explanation for observed differences in mortgage loan performance between bank and nonbank lenders.     

A Model of Mortgage Default

In this paper, we solve a dynamic model of households' mortgage decisions incorporating labor income, house price, inflation, and interest rate risk. Using a zero‐profit condition for mortgage lenders, we solve for equilibrium mortgage rates given borrower characteristics and optimal decisions. The model quantifies the effects of adjustable versus fixed mortgage rates, loan‐to‐value ratios, and mortgage affordability measures on mortgage premia and default. Mortgage selection by heterogeneous borrowers helps explain the higher default rates on adjustable‐rate mortgages during the recent U.S. housing downturn, and the variation in mortgage premia with the level of interest rates.     

How Unsecured Credit Policies Influence Mortgage and Unsecured Loan Defaults

Before the global financial crisis, the proportion of households defaulting on the mortgage while remaining current on the unsecured loan was almost the same as the proportion of households current on the mortgage but defaulting on the unsecured loan. After the crisis, the former ratio became higher than the latter. By using a heterogeneous agent model with the mortgage and the unsecured loan, I examine how the order of defaults changed before and after the crisis. I then analyze the impacts of unsecured credit policies on households' mortgage and unsecured loan defaults. My quantitative exercise shows that both default rates can decrease as the cost for unsecured loan defaults increases.     

Household Leverage

I propose a life‐cycle model where a finitely lived risk‐averse household finances its housing investment by opting to provide a down payment. Given that the household may default, risk‐neutral lenders efficiently charge a default premium to hedge against expected losses. This has two major consequences. First, the higher the house price volatility, the higher the down payment the household provides to decrease the volatility of the equity share in the house. Second, in the presence of borrowing constraints, higher risk of unemployment persistence and/or a substantial drop in labor income decreases the leveraged position the household takes on.     

Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation

We use a contingent claims framework for valuing the the default and prepayment embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). This methodology provides a template for the borrower, lender, and insurer to compare mortgage terms, including the fairness of contract rates, arrangement fees, prepayment penalties, any MIG premiums required, and co-insurance exposure. With empirical inputs, this model may eventually be useful as a mark-to-value proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining valued added accounting, appropriate reserves, and indeed for setting premiums and business drivers. Fixed-rate endowment mortgages differ from fixed-rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We compare endownment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatilities.     

The Effect of Mortgage Price and Default Risk on Mortgage Spreads

Variations over time in mortgage yield spreads should reflect changes in the underlying prepayment option value; moreover, the relationship between mortgage yield spreads and interest rate dynamics should weaken as the value of the borrowers prepayment option declines. We verify this hypothesis through an empirical analysis of residential mortgage yield spread behavior, and we also present evidence that the strength of the relationship between mortgage spreads and interest rate dynamics weakens (strengthens) as the level of default risk increases (decreases). This result is consistent with the competing risks effect between a borrowers option to prepay or default. Our results demonstrate the importance of accounting for mortgage price discount to par as well as default risk when developing time series of mortgage yields.     

Signaling-Screening Equilibrium in the Mortgage Market

The signaling model of Spence (1973a) and the screening model of Rothchild and Stiglitz (1976) have been separately used to explain economic phenomena when there is asymmetric information. In the real world, however, situations of asymmetric information often simultaneously involve signaling and screening. In this paper, we combine signaling and screening mechanisms and demonstrate a signaling-screening separating equilibrium. We present the analysis within the framework of mortgage markets. Borrowers signal their default risk types to lenders by acquiring different credit records. This partially separates borrowers into subsets. Lenders screen each subset by offering menus of mortgage loan contracts. Borrowers, then, self-select by choosing particular contracts from the menu. We show the conditions under which the signaling-screening equilibrium is Pareto superior to a screening-only equilibrium.     

Optimal Put Exercise: An Empirical Examination of Conditions for Mortgage Foreclosure

Implicit in option-pricing models of mortgage valuation are threshold levels of put-option value that must be crossed to induce borrower default. There has been little research into what these threshold values are that come out of pricing models or how they compare to exercised option values seen in empirical data. This study decomposes boundary conditions for optimal default exercise to look at the economic dynamics that should lead to optimal default timing. Empirical data on FHA insured mortgage foreclosures is then examined to discern the predictive influence of optimal-option-valuation-and-exercise variables on observed default timing and values. Interesting results include a new understanding of how to measure and use property equity variables during economic downturns, house-price index ranges over which default is exercised for various classes of borrowers, and implied differences in appreciation rates between market-price indices and foreclosed properties.     

住房贷款违约风险定量分析初探

本首先剖析了影响住房贷款违约风险的主要因素，然后引入Merton的结构化模型来分析住房贷款在等额偿还方式下违约风险的度量问题，并从横向和纵向两个角度，通过模拟计算得出房价波动率和无风险利率对住房贷款的违约概率、预期损失和违约风险溢价的影响规律以及这三个指标在贷款期内的变化规律。     

Differential Impacts of Structural and Cyclical Unemployment on Mortgage Default and Prepayment

The Great Recession (the fourth quarter of 2007 through the second quarter of 2009) has been characterized by high rates of foreclosures and unemployment. Using a sample of community reinvestment loans, we examine the impact of structural unemployment and cyclical unemployment on mortgage terminations (default and prepayment). We find that mortgage default and prepayment are more sensitive to changes in the structural component of the local unemployment rate than in the cyclical component. In addition, depending on whether structural unemployment rates are high or low, borrowers and lenders react differently to the incentives to terminate a loan.     

Credit Scoring and Mortgage Securitization: Implications for Mortgage Rates and Credit Availability

This article develops a model of the interactions between borrowers, originators, and a securitizer in primary and secondary mortgage markets. In the secondary market, the securitizer adds liquidity and plays a strategic game with mortgage originators. The securitizer sets the price at which it will purchase mortgages and the credit-score standard that qualifies a mortgage for purchase. We investigate two potential links between securitization and mortgage rates. First, we analyze whether a portion of the liquidity premium gets passed on to borrowers in the form of a lower mortgage rate. Somewhat surprisingly, we find very plausible conditions under which securitization fails to lower the mortgage rate. Second, and consistent with recent empirical results, we derive an inverse correlation between the volume of securitization and mortgage rates. However, the causation is reversed from the standard rendering. In our model, a decline in the mortgage rate causes increased securitization rather than the other way around.     

个人住房抵押贷款违约风险跃迁概率研究

巴塞尔新资本协议提出针对个人住房抵押贷款可采用内部评级高级法评估其风险,在满足某些最低条件和披露要求的前提下,商业银行可根据自己对个人住房抵押贷款违约概率、违约损失率、违约风险暴露和期限等要素的估计值确定相应的资本要求。本文提出将风险跃迁概率引入到对个人住房抵押贷款提前还款-违约概率的定量估计中。借助逻辑斯特模型,本文将这一概念实际运用到对个人住房抵押贷款微观数据的分析当中,得到的实证研究结论包括借款人历史还款状态可以作为表征其未来还款状态的重要指标,贷龄与借款人还款状态的跃迁概率显著相关等。     

An Early Assessment of Residential Mortgage Performance in China

The residential mortgage market becomes a financial engine for the booming residential housing development and sustained economic growth in China. Our study provides the first rigorous empirical analysis on the earlier performance of residential mortgage market in China based on a unique micro dataset of mortgage loan history collected from a major residential mortgage lender in China. We found that while the option theory fails to explain prepayment and default behavior in the residential mortgage market in China, other non-option theory related financial economic factors play major roles in determining the prepayment and default risks in China. We also found that borrower’s characteristics are significant in determining prepayment behavior, hence may be used as an effective tool for screening potential high risk borrowers in the loan origination process. Adopting a risk-based pricing in residential mortgage lending in China can improve the efficiency of the market, and enhance the credit availability to the most needed households, i.e., the younger households, blue-collar workers, lower income households, and help them become homeowners.     

Collateral Risk in Residential Mortgage Defaults

This paper presents a systematic framework for capturing the collateral-driven mortgage default risk. A forward-looking home price distribution model is developed that explicitly incorporates different sources of volatility in the market value of collateral houses. A consistent and computationally-efficient top-down approach of home price simulation is also introduced. We show that with the proper inclusion of all relevant sources of volatilities, the top-down approach provides close approximation to the results generated by a theoretically sound but computationally demanding bottom-up simulation approach. Using a numerical simulation, we demonstrate that a geographically-diversified mortgage pool entails a substantially lower level of systematic collateral driven mortgage default risk compared to a spatially-concentrated pool. However, the expected default risk is shown to remain unaffected, indicating that the benefit from geographic diversification is only realized through lower risk-based capital requirements, not in lower mortgage insurance premiums. Based on the US state level house price indices, the systematic risk of a state-concentrated mortgage pool is estimated to be about four times higher than that of a nationally-diversified mortgage pool. Our results also show that, among the different volatility components, omitting the cross-sectional dispersion of individual home prices would produce the largest bias in assessing home-price-based mortgage default risk.