Unobservable heterogeneity and rational learning: Pool-specific versus generic mortgage-backed security prices

Previous mortgage prepayment and valuation models assume that two mortgage pools with the same observable characteristics should behave indistinguishably. However, even pools with apparently identical characteristics often exhibit markedly different prepayment behavior. The sources of this heterogeneity may be unobservable, but we can infer information about a pool from its prepayment behavior over time. This article develops a methodology for using this information to calculate pool-specific mortgage-backed security prices. Knowledge of these prices is important both for portfolio valuation and for determining the cheapest pool to deliver when selling mortgagebacked securities. We find that unobservable heterogeneity between mortgage pools is statistically significant, and that pool-specific prices, calculated for a sample of outwardly identical mortgage pools between 1983 and 1989, may differ greatly from any single representative price.     

A Dynamic Analysis of Fixed- and Adjustable-Rate Mortgage Terminations

This paper provides a side-by-side comparison of loan-level statistical models for fixed- and adjustable-rate mortgages. Multinomial logit models for quarterly conditional probabilities of default and prepayment are estimated. We find that the estimated impacts of embedded option values for prepayment and default are generally quite similar across both FRM and ARM loans, providing additional empirical support for the basic predictions of the options theory. We also find that differences in estimates of conditional probabilities of prepayment and default associated with mortgage age, origination period, original LTV, and relative loan size, indicate the continued significance of these other economic and demographic factors for empirical models of mortgage terminations.     

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 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.     

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 probability of fixed- and adjustable-rate mortgage termination

This article analyzes mortgage terminations using a national individual loan data set for the 1986–1992 period. The standard option-choice-theoretic framework is supplemented with variables to proxy for non-option-related termination determinants. Separate multinominal logit models are estimated for three mortgage types: 30-year FRMs, 15-year FRMs, and 30-year ARMs. The results indicate substantial differences in the response of the mortgage types to variables included in the model. FRM15 prepayments are the most responsive to prepayment option values; FRM30 prepayments are less responsive to option values and are dirven by local area housing market and economic conditions; ARM prepayment rates are higher but defeult rates are lower relative to the FRMs. A noteworthy finding is that teaser discounts reduce the likelihood of ARM defaults.     

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.     

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.     

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.     

Endogenous current coupons

We consider the problem of identifying current coupons for agency-backed to-be-announced pools of residential mortgages. Such coupons, or mortgage origination rates, ensure par-valued pools. In a doubly stochastic reduced form model which allows prepayment intensities to depend upon both current and origination mortgage rates, as well as underlying investment factors, we identify the current coupon as a solution to a degenerate elliptic, nonlinear fixed point problem. Using Schaefer’s theorem, we prove existence of a current coupon. We also provide an explicit approximation to the fixed point, valid for compact perturbations off a baseline factor-based intensity model. A numerical example is provided which shows that the approximation performs well in estimating the current coupon.     

The timing of prepayment: A theoretical analysis

This article develops the analytical methods necessary to determine the prepayment patterns of a mortgage contract. The most obvious measure of how many years a mortgage is likely to last is the expected time to termination. It is this measure that we most fully explore. However, since the method employed is able to characterize the probability of prepayment in any given time period, the means is provided to determine any measure of the time to termination.     

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.     

What Drives Default and Prepayment on Subprime Auto Loans?

This paper uses novel data on the performance of loan pools underlying asset-backed securities to estimate a competing risks model of default and prepayment on subprime automobile loans. We find that prepayment rates increase rapidly with loan age but are not affected by prevailing market interest rates. Default rates are much more sensitive to aggregate shocks than are prepayment rates. Increases in unemployment precede increases in default rates, suggesting that defaults on subprime automobile loans are driven largely by shocks to household liquidity. There are significant differences in the default and prepayment rates faced by different subprime lenders. Those lenders that charge the highest interest rates experience the highest default rates, but also experience somewhat lower prepayment rates. We conjecture that there is substantial heterogeneity among subprime borrowers, and that different lenders target different segments of the subprime market. Because of their higher default rates, loans that carry the highest interest rates do not appear to yield the highest expected returns.     

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.     

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.     

INTEREST RATE RISK HEDGING FOR DUE-ON-SALE MORTGAGES WITH EARLY TERMINATION

The impact of random early termination on the interest rate elasticity and the related implications of hedging a mortgage security are examined. The common approach to computing duration using average mortgage life is shown to be biased and insufficient. Because the prepayment distributions of mortgages tend to have wide dispersions, substantial errors result from using average mortgage life. These results are also applicable to other financial obligations subject to prepayment.     

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.     

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.     

Subprime Mortgage Defaults and Credit Default Swaps

We offer the first empirical evidence on the adverse effect of credit default swap (CDS) coverage on subprime mortgage defaults. Using a large database of privately securitized mortgages, we find that higher defaults concentrate in mortgage pools with concurrent CDS coverage, and within these pools the loans originated after or shortly before the start of CDS coverage have an even higher delinquency rate. The results are robust across zip code and origination quarter cohorts. Overall, we show that CDS coverage helped drive higher mortgage defaults during the financial crisis.     

Frictions, Heterogeneity and Optimality in Mortgage Modeling

The purpose of this article is to provide a unified framework for incorporating frictions into a theoretical options-pricing model (OPM) for mortgages. This article presents formulation for a frictions-adjustable mortgage model that integrates borrower heterogeneity while simultaneously preserving prepayment and default financial decisions. Our model demonstrates the flexibility of the OPM by simulating separate and concurrent effects of three categories of frictions on the mortgage and mortgage components. Researchers can use our example formulation to determine the effects of specific borrower characteristics on mortgage values without destroying the options theoretic framework.