Commercial Mortgage-Backed Securities: Prepayment and Default

One of the major developments in real estate finance during the 1990s was the emergence of a viable market for commercial mortgage backed securities. The growth in this market has spurred greater interest in empirical and theoretical research on commercial mortgage default and prepayment. We employ a competing risks model to examine the default and prepayment behavior of commercial loans underlying CMBS deals. We find that changes in the yield curve have a direct impact on the probability of mortgage termination. Furthermore, we do not find any statistical relationship between LTV and prepayment or default.     

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.     

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.     

SECONDARY MORTGAGE MARKET PURCHASE COMMITMENT YIELDS

We provide empirical evidence that quoted secondary market mortgage yields conform to the predictions of option theory. We compare Fannie Mae and Freddie Mac origination yields offered in the secondary market from 1985 to 2003 with the predictions of a two‐state binomial mortgage option valuation model. Our two‐state approach considers a mean‐reverting interest rate process as well as a stochastic housing price. Using predictions from option simulations, we find strong links between market practice and mortgage option prepayment and default factors over time. We also find cross‐sectional differences that are consistent with the institutional structure of the markets.     

On the determinants of yield spreads between mortgage pass-through and Treasury securities

Yield spreads between mortgage pass-through and U.S. Treasury securities may reflect differences in taxation, phenomena affecting relative supply and demand, and compensation for default, call, and marketability risks on mortgage instruments. Our research empirically models differences in yields between pass-throughs and comparable-maturity Treasuries. We find that interest-rate volatility and the term structure of rates, factors often cited in the mortgage pricing literature as affecting the mortgage call premium, are the primary determinants of movements in these spreads. Moreover, these effects have grown in importance in recent years as exercise of the prepayment option has increased. We also find evidence that liquidity and credit concerns affect the pricing of pass-through securities.     

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.     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

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.     

An empirical analysis of home equity loan and line performance

Given the growth in home equity lending during the 1990s, it is imperative that lenders and regulators understand the risks associated with this segment of the residential mortgage market. Using a unique panel data set of over 135,000 homeowners with second mortgages, our analysis indicates that significant differences exist in the prepayment and default probabilities of home equity loans and lines, providing insights into bank minimum capital requirements. We find that households with equity loans are relatively more sensitive to changes in interest rates. By contrast, households with equity lines are more sensitive to appreciation in property value.     

Private information and incentives: Implications for mortgage contract terms and pricing

We examine the linkage in equilibrium among (1) contract design; (2) expected prepayment and default likelihoods; and (3) the pricing of mortgage contracts by focusing upon the effects of the borrower's private information at the time of contracting. We examine the implications of these perspectives upon the empirical analysis of prepayment behavior and use the framework to examine the predominance of long-term mortgage contracts in the United States. We consider examples that explore the trade-offs between fixed and adjustable rate instruments, assumable and due-on-sale loans, and contract interest rates and initial discounts (points).     

Credit Counseling and Mortgage Termination by Low-Income Households

Published research on credit counseling and mortgage termination is surprisingly scarce, despite substantial growth in this industry. While the purpose of counseling is to assist low-income borrowers to improve their handling of debt and thereby reduce default, counseling may also improve the borrowers understanding of their financial position and thus induce optimal mortgage termination. Using a competing-risks framework, we study the effects on default and prepayment of a counseling program implemented in several Midwest states. We find weak evidence of that the default hazard was lower for graduates of the counseling program, but that their default behavior was more optimal. The prepayment hazard was higher for counseled borrowers, but their prepayment behavior was not more optimal. Overall, counseling seems to affect the lenders profits, but the net effect should be evaluated both in terms of prepayment and default.     

Modeling conventional residential mortgage refinancings

This article models fixed-rate mortgage refinancings and offers an empirical test of the model. The model relates the probability that a household prepays its residential mortgage to both financial and economic variables. The financial variables included in the model measure the value of the embedded call option present in conventional fixed-rate mortgage loans. The economic variables measure the household's propensity to prepay for housing consumption adjustment reasons. Our main empirical finding is that increased interst-rate volatility significantly decreases prepayment probability. In addition, we find some statistical evidence to support the hypothesis that prepayment rates increase with increases in household income, increases in household size, and vary by age of household head and regionally.     

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.     

Valuation of Residential Mortgage-Backed Securities with Default Risk Using an Intensity-Based Approach

This paper develops a valuation model for fixed-rate mortgages, mortgage pools, and residential mortgage-backed securities (RMBS's) using an intensity-based approach. This model incorporates full prepayment, partial prepayment, and default in valuing a mortgage. Full prepayment is further classified into “refinancing” and “sale of a house” depending on the reason. The time of occurrence of each of these three types of prepayment and default is modeled as the first jump time of a Cox process. Under these conditions, the valuation formula for a mortgage as well as a partial differential equation (PDE) that the mortgage value satisfies is provided. As for implementation of the model, the short-term riskless interest rate and the house price are adopted as state variables. Each intensity process is specified in a manner that allows a jump in intensity depending on the state variables and the borrower's incentive for prepayment or default. Through such specifications, it is shown that our model has characteristics similar to some structural models in previous literature. As for the numerical method for valuation, we propose a simple backward induction technique on a tree instead of the commonly used Monte Carlo method. Additionally, the method for estimating the model is discussed, and the results of numerical simulations are reported.This paper represents the view of the author and does note necessarily the views of the Mitsubishi UFJ Securities Co., Ltd. or members of its staff.     

Estimating the marginal contribution of adjustable-rate mortgage selection to termination probabilities in a nested model

In this study we measure the marginal contribution of ARMs to termination probabilities. To do this we develop a modified nested-logit model of mortgage selection and termination and identify the role of risk aversity in the selection process. Simulations of termination probabilities under different economic scenarios indicate how ARMs decrease overall portfolio risk through declines in prepayment probabilities which more than offset the increases in default probabilities associated with them.     

Omitted Mobility Characteristics and Property Market Dynamics: Application to Mortgage Termination

Property market dynamics depend on changes in long run equilibrium and on impediments to adjustment towards equilibrium. Mortgage termination due to mobility, default and refinancing provides a lens for evaluating property market adjustments. The borrower’s decision to move as an adjustment mechanism in the property market is associated with utility-maximizing decisions to either prepay or default on the mortgage. The optimal choice between these two termination events may depend on unobserved propensities related to change in income, job location, or family size, and substantial inertial forces including search costs, neighborhood change and attachment to an area. We propose a method for modeling variables determining the impact of mobility on mortgage terminations with imperfect household and loan level data. Since omitted variables contribute to moving decisions and therefore to mortgage prepayment and default decisions, utility functions for sale and default are correlated through these unobservable variables; thus, the IIA assumption of the widely used Multinomial Logit Model (MNL) is violated. Under such circumstances, econometric theory suggests that the Nested Logit Model (NMNL) is a better choice, which obviates the limitation of MNL by allowing correlation in unobserved factors across alternatives. Using loan level micro data, we find empirical evidence showing significant correlation between sale and default due to omitted borrower mobility characteristics. Our simulations find that NMNL out performs MNL in out-of-sample prediction. Improved predictions of moves and defaults are applicable to micro and macro analysis of the housing market system.     

Bias in estimates of discrimination and default in mortgage lending: The effects of simultaneity and self-selection

The common practices of estimating single-equation models of mortgage rejection to test for discrimination in mortgage markets or single-equation ex ante mortgage default equations to validate underwriting criteria produce biased and inconsistent parameter estimates. This is due to problems of simultaneous equations bias which arise because, in a world of imperfect information, mortgage terms are not exogenous to the rejection or default decision. In addition, mortgage default estimates are also subject to selection bias. Monte Carlo experiments are used to study the nature and extent of likely bias in single-equation estimation results. We find that rejection equation estimates indicate discrimination when none exists and that estimated coefficients of mortgage terms, such as the loan-to-value ratio, are also subject to significant bias in both rejection and default equations.     

Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.     

Mortgage Pricing Implications of Prepayment: Separating Pecuniary and Non-pecuniary Prepayment

The Journal of Real Estate Finance and Economics - In the study of mortgage loan pricing, prepayment and default hazards are considered. While default results in loss of initial capital, prepayment...     

Characteristics of Mortgage Terminations: an Analysis of a Loan-Level Dataset

Understanding mortgage termination behavior is crucial for valuating mortgage-backed securities. Analyzing a unique loan-level dataset, this study examines the characteristics of mortgage prepayment and default behaviors in the Korean housing and housing finance markets. We also analyze mortgage termination behaviors across regions, loan purposes, and periods. The results suggest that the prepayment rate of fixed-rate mortgages (FRMs) and the ratio of adjustable-rate mortgages to FRMs can provide meaningful signals for the Korean household economy. Although the macro-prudential policies pertaining to the loan-to-value ratio (LTV) and debt-to-income ratio (DTI) are very effective, their effects can vary depending on the region or loan purpose. Furthermore, the DTI and credit score cannot always identify the default risks of mortgages not intended for housing purchases even though such mortgages are more vulnerable to macroeconomic changes. The observed changes in default behavior indicate that the government’s policies to promote fixed-rate loans have achieved a certain degree of success.