The role of prepayment penalties in mortgage loans

We study the effect of mortgage prepayment penalties on borrowers’ prepayments and delinquencies by exploiting a 2007 reform in Italy that reduced penalties on outstanding mortgages and banned penalties on newly-issued mortgages. Using a unique dataset of mortgages issued by a large Italian lender, we provide evidence that: 1) before the reform, mortgages issued to riskier borrowers included larger penalties; 2) higher prepayment penalties decreased borrowers’ prepayments; and 3) higher prepayment penalties did not affect borrowers’ delinquencies. Moreover, we find suggestive evidence that prepayment penalties affected mortgage pricing, as well as prepayments and delinquencies through borrowers’ mortgage selection at origination, most notably for riskier borrowers.     

The probability of prepayment

Prepayment is a risk of holding a mortgage or derivative security. Incorrect pricing of prepayment risk leads to increased volatility and uncertainty in mortgage security markets. This article prices prepayment risk within an underlying callable bonds model. To price mortgages accurately, a probability of prepayment is required. A mortgage is a callable bond with a package of an option to prepay currently and a sequence of options to prepay up to the date of maturity. This sequence is summarized by a compound option. The probability of prepayment is determined by the prices of the current call and this compound option. These option prices depend on market interest rates and age, and on the contract terms of the originated mortgage.     

Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.     

The inefficiency of refinancing: Why prepayment penalties are good for risky borrowers

This paper provides a theoretical analysis of the efficiency of prepayment penalties in a dynamic competitive lending model with risky borrowers and costly default. When considering improvements in the borrower's creditworthiness as one of the reasons for refinancing mortgages, we show that refinancing penalties can be welfare improving and that they can be particularly beneficial to riskier borrowers in the form of lower mortgage rates, reduced defaults, and increased availability of credit. Thus, a high concentration of prepayment penalties among the riskiest borrowers can be an outcome of efficient equilibrium in a mortgage market. We also provide empirical evidence that is consistent with the key predictions of our model.     

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.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

Commercial Mortgage Workout Strategy and Conditional Default Probability: Evidence from Special Serviced CMBS Loans

This study recognizes that commercial mortgage default is not a one-step process and examines a previously under explored aspect in the whole default process, that is the stage between the initial delinquency and default. We distinguish the servicers’ behavior from the borrowers’ behavior. A multinomial logit model is applied to analyze the servicers’ choice of workout options and a proportional hazard model is applied to analyze the borrower’s default decision-making process under time-varying conditions. We find that cash flow condition is the most significant factor in the servicers’ decision making process. We also find that borrowers make default decisions based upon both the equity position in the mortgage and the cash flow condition in the space market. Key real estate space market variables, such as market-level vacancy rates, also provide useful information in explaining commercial mortgage defaults. We find that special service seems to be successful in reducing the probability that a troubled loan will default. Finally, sensitivity analysis shows nontrivial economic significance of the impact of explanatory variables, real estate market variables in particular have the most significant impact on the pricing of special-serviced loans.     

Unintended Consequences of Risk Based Pricing: Racial Differences in Mortgage Costs

The following analysis focuses on the role that risk pricing has had in the allocation and access to mortgage funds, specifically how it results in cost differences by race. Using a sample of fixed-rate first lien mortgages, we control for the risk characteristics of borrowers and assets. We find that borrowers with comparable credit quality experience significantly higher costs for mortgages in neighborhoods with a high density of minority households. Further, when the pricing differential is controlled for in a model of mortgage default, there is no support for neighborhood price differences. This finding illustrates a potential inequity that results from efficient/risk pricing in mortgage underwriting.     

A New Prepayment Model (with Default): An Occupation-time Derivative Approach

A new prepayment model is developed, which improves the modeling of the borrowers decision process by incorporating an occupation-time derivative in the valuation framework of a fixed-rate mortgage. This option-theoretic mortgage valuation model is based on stochastic house-price and interest-rate models, and requires a particularly subtle technique to incorporate a new type of occupation-time derivative, where the barrier (which activates the derivative) is in the value process and not the underlying process (as it is in standard occupation-time derivatives). This new model simulates a delay in prepayment by the borrower (beyond the time simple ruthless prepayment dictates), thus increasing the value of the mortgage to the lender, compared to the value gained using more basic models. This allows for a more advanced borrower decision process, where a rational exercise structure is retained in a modified form. Empirical evidence supports this theory, which should be beneficial for accurate mortgage-backed security pricing. The results in this paper explore thoroughly the effect on the mortgage value of a delay in prepayment by the borrower on the embedded options held and on the insurance component.

An Analysis of Mortgage Termination Risks: A Shared Frailty Approach with MSA-Level Random Effects

Investigating the residential mortgage defaults and prepayments has been the subject of research for the past three decades. The literature on mortgage default and prepayment is often used to inform credit risk policies and asset pricing strategies. This literature has evolved from the use of logistic regressions to the use of survival and frailty models that control for unobserved heterogeneity. In this paper, we apply a shared-frailty survival model to analyze the mortgage termination risks. In particular, we investigate whether mortgages originated in the same Metropolitan Statistical Area (MSA) share common unobserved factors and how these factors affect the mortgage termination risks. The paper demonstrates that MSA-level frailty, together with other risk factors, has significant effects on the probability of mortgage terminations risks.     

Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.     

Rational prepayment and the valuation of mortgage-backed securities

This article presents a new model of mortgage prepayments, basedon rational decisions by mortgage holders. These mortgage holdersface heterogeneous transaction costs, which are explicitly modeled.The model is estimated using a version of Hansen's (1982) generalizedmethod of moments, and is shown to capture many of the empiricalfeatures of mortgage prepayment. Estimation results indicatethat mortgage holders act as though they face transaction coststhat far exceed the explicit costs usually incurred on refinancing.They also wait an average of more than a year before refinancing,even when it is optimal to do so. The model fits observed prepaymentbehavior as well as the recent empirical model of Schwartz andTorous (1989). Implications for pricing mortgage-backed securitiesare discussed.     

Choosing between fixed-and adjustable-rate mortgages: The case of commercial mortgages

This article reports on the determinants of the ARM choice for commercial real estate projects. The theoretical literature suggests that commercial real estate projects are more likely to be financed with an adjustable-rate mortgage (ARM) if the project's income stream or value is expected to rise with inflation over time. The empirical model estimated is a structural probit probability model of the ARM choice. Our results demonstrate that commercial borrowers typically place great emphasis on relative interest-rate differentials when deciding which mortgage is best. We also find that commercial mortgage borrowers will ordinarily be reluctant to issue an ARM when the fixed interest rate is low.     

Residential Mortgage Lending and Borrower Risk: The Relationship Between Mortgage Spreads and Individual Characteristics

The mortgage banking environment in Hong Kong is quite different from that in the United States. For example, the secondary mortgage market and mortgage insurance only started after 1997. Using a large data set on mortgages, we examine empirically how mortgage rates in this market vary with various individual borrower, property, and loan characteristics. We find that mortgage rates in Hong Kong do vary with individual characteristics, which suggests credit sorting according to both prepayment risk and default risk, as a higher mortgage rate is found to be related to either higher collateral (a lower loan-to-value ratio) or slower prepayment. The empirical results suggest that lenders in Hong Kong can observe the risk type of individual borrowers to a certain extent and charge a corresponding mortgage spread. Overall, the evidence is consistent with the sorting-by-observed-risk paradigm as in Berger and Udell (1990).     

Legal Restrictions in Personal Loan Markets

This study examines the pricing of personal loans in the form of second mortgages to determine whether state-specific default laws have an effect on the availability and cost of that debt. We examine the pricing of loans to higher risk borrowers and whether borrowers in states that limit lender ability to seek default remedies pay higher credit costs. Our results indicate that, for the most part, lenders rationally price loans to higher risk borrowers. However, when we focus on borrowers with low credit scores, the results indicate that mean actual loan rates are higher than those predicted by our model. The results also indicate that state-specific default laws have an effect on the price of credit. Finally, the results show that there is a greater degree of error in the pricing of second mortgage loans to borrowers with low credit scores than to borrowers with high credit scores.     

Predicting Prepayment and Default Risks of Unsecured Consumer Loans in Online Lending

Online lending provides a means of fast financing for borrowers based on their creditworthiness. However, borrowers may undermine this agreement due to early repayment or default, which are two major concerns for the platform and lenders, since both affect the profitability of a loan. While default risk is frequently focused on credit scoring literature, prepayment has received much less attention, despite a higher prepayment rate being observed in online lending when compared with default. This article uses multivariate logistic regression to predict the probability of both the underlying prepayment and default risks. Real consumer lending data of 140,605 unsecured loans provides evidence that these two events have their own distinct patterns. We consider systemic risk by incorporating macroeconomic factors in modeling and address the influence of economic conditions, which are lessons learnt from the last financial crisis. The out-of-sample validation has shown that both prepayment and default can be accurately predicted. This article highlights the necessity of regulations on prepayment given the fast growing online lending market.     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

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.     

Housing-Price Cycles and Prepayment Rates of U.S. Mortgage Pools

Empirical mortgage prepayment models generally have trouble explaining differences in mortgage-prepayment speeds among pools with similar interest rates on the underlying mortgages. In this article, we model some of the sources of termination heterogeneity across mortgage pools, particularly the role of regional variations in housing prices in generating atypical prepayment speeds. Using a sample of Freddie Mac mortgage pools from 1991 to 1998, we compare two classes of empirical models: a rational option-pricing model using a backward-solving pricing algorithm and an empirical hazard model. In both empirical estimation strategies, we find evidence that differences in house-price dynamics across regions are an important source of between-pool heterogeneity. This finding is then shown to be robust to alternative ways of parameterizing pool heterogeneity in mortgage termination models.     

Interest-only and principal-only mortgage strips as interest-rate contingent claims

Interest-only (IO) and principal-only (PO) mortgage strips are valued in a stochastic interest-rate environment. The prepayment rate of the underlying mortgages is affected by two considerations not present in the pure financially rational model: (1) The property owner's holding period is assumed to follow a Gamma distribution, resulting in the possibility of prepayment due to the sale of the property (i.e., prepayment that is too early based on market interest rates); and (2) borrowers are assumed to face heterogeneous transaction costs related to refinancing the existing mortgage, and delay refinancing when market conditions make it optimal to do so (refinancing too late). Properties of IO/PO strips are identified by the finite difference method.