Time-Varying Mortgage Prepayment Penalties

Recent empirical findings reveal that prepayment decisions of commercial property owners are slower than predicted by the pure options-pricing model (OPM). Borrower decisions appearing slow, however, may be quite rational when prepayment penalties of a time-varying nature are incorporated into the OPM. This article uses a competing risks OPM, adjusted for each of four different categories of prepayment penalties, to analyze borrower prepayment behavior. We find the value of delaying prepayment is often higher for mortgages with declining-rate penalties than for mortgages with static-rate penalties, frequently requiring a substantially higher interest rate spread to trigger a refinance. Multifamily loan prepayment records reveal the type of prepayment pattern that the adjusted OPM indicate should occur, reducing the gap between empirical findings and theoretical predictions. The results have implications for the specification of regressions fit to historical data, for the pricing of newly originated commercial mortgages, and for pricing in the single-family market where prepayment penalties are reemerging.     

An Analysis of Mortgage Contracting: Prepayment Penalties and the Due-on-Sale Clause

The due-on-sale clause contained in most conventional home mortgage contracts is equivalent to a prepayment penalty equal to the difference between the face value and market value of the loan. We analyze a bilateral game with asymmetric information and show that the bank demands the full penalty unless the market value of the loan is sufficiently low. In that case, the bank demands a prepayment penalty which is independent of the market value of the loan in order to induce additional prepayments. We also demonstrate, by a risk-sharing argument, that the due-on-sale clause is optimal in some settings, even though it eliminates some beneficial home sales.     

Mortgage contract design and systemic risk immunization

This paper provides theoretical results for the design of contracts used in the market for residential household mortgages and mortgage securities. Critical elements in the problem of immunizing systemic risk through efficient contract design are identified. Using an extension of classical immunization theory, this paper demonstrates that systemic risk of long amortization mortgage contracts is reduced when term to maturity of the contract at origination is significantly less than the amortization period. In addition, incorporating prepayment and limited recourse default options into the mortgage contract increases systemic risk when compared with full recourse mortgage contracts having yield maintenance prepayment penalties. The theoretical results are used to evaluate the systemic risk management problems that have plagued the US mortgage funding system.     

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.     

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.     

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).     

Optimal student loans and graduate tax under moral hazard and adverse selection

We characterize the set of second‐best “menus” of student‐loan contracts in an economy with risky labor‐market outcomes, adverse selection, moral hazard, and risk aversion. We combine student loans with optimal income taxation. Second‐best optima provide incomplete insurance because of moral hazard. Optimal repayments must be income contingent, or the income tax must comprise a graduate tax. Individuals are ex ante unequal because of differing probabilities of success, and ex post unequal, because taxation trades off incentives and redistribution. In addition, second‐best optima exhibit an interim equalization property: the poststudy but prework expected utilities of newly graduated student types must be equal.     

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.     

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.     

Prohibitions on punishments in private contracts

In most contemporary economies loan contracts that mandate exclusionary penalties such as imprisonment or other non-pecuniary punishments for defaulting debtors are illegal, despite the fact that in some cases contracting parties might gain by being able to use them. A possible rationale for contracting restrictions of this type is that exclusion imposes negative externalities on individuals not party to the original loan contract. We explore the ability of such externalities to account for these restrictions. We contrast exclusion with enforceable collateral seizure, a widespread feature of developed financial systems. We also consider “behavioral” agents who underestimate their chances of being punished, and show that overconfidence of this type is a less compelling justification for restrictions on exclusionary punishments than is often argued.     

Valuation of Mortgage Servicing Rights with Foreclosure Delay and Forbearance Allowed

We develop a bivariate binomial model to price Mortgage Servicing Rights (MSRs). Our model is an improvement over previous MSR pricing models by explicitly incorporating the realistic assumptions that there are additional costs involved in servicing delinquent loans. In addition to the Hilliard et al. mortgage-pricing tree, we extend additional sub-branches to model the borrower's decision of prepayment, cure, and foreclosure after a loan becomes delinquent. We then investigate how the value of the Mortgage Servicing Right varies with interest rate volatility, house price volatility, delinquency options, deficiency judgments, default penalties, forbearance periods, and speed of adjustments factors. JEL Classification: C15, G21     

Mortgage risks,debt literacy and financial advice

A limited understanding of mortgage contracts and the risks involved may have contributed to the outbreak of the 2007–2008 financial crisis. We developed a special questionnaire relating mortgage loan decisions to financial knowledge and financial advice. Our results demonstrate that homeowners appear to be well aware of mortgage risks. Large loans relative to home value are perceived as riskier, as are loans with large mortgage payments relative to income and loans linked to investment vehicles. Homeowners with riskier mortgages indicated that they could encounter financial problems should house prices or their income decline. Homeowners with relatively low debt literacy are more likely to take out traditional mortgages with principal repayments over the maturity of the loan. Riskier mortgages are more prevalent among homeowners with a better understanding of loan contracts. Financially less sophisticated homeowners consulting mortgage brokers, too, hold riskier mortgages.     

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.     

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.     

The voluntary adoption of International Financial Reporting Standards and loan contracting around the world

Using a sample of non-U.S. borrowers from 40 countries during 1997 through 2005, this paper investigates the effect of the voluntary adoption of International Financial Reporting Standards (IFRS) on price and nonprice terms of loan contracts and loan ownership structure in the international loan market. Our results reveal the following. First, banks charge lower loan rates to IFRS adopters than to non-adopters. The difference in loan rates in excess of a benchmark rate between the two groups is about 20 basis points for all loans and nearly 31 basis points for London Interbank Offered Rate (LIBOR)-based loans. Second, banks impose more favorable nonprice terms on IFRS adopters, particularly less restrictive covenants. We also provide evidence suggesting that banks are more willing to extend credit to IFRS adopters through larger loans and longer maturities. Finally, IFRS adopters attract significantly more foreign lenders participating in loan syndicates than non-adopters.     

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.     

Valuing mortgage loan servicing

We develop an intertemporal model for valuing mortgage loan servicing contracts. The model includes a stochastic short-term interest rate and realized inflation rate which jointly determine the current mortgage coupon rate, the mortgagor's prepayment decision, the servicer's future net cash flows, and the rate at which to discount these future cash flows. Several potential uses of the model for institutions that service mortgages and trade servicing portfolios are illustrated by the application of the model to servicing fixed-rate mortgages and adjustable-rate mortgages. The model also is applicable to regulatory issues and to the servicing of other types of loans.The authors gratefully acknowledge support from the Federal Home Loan Bank Board, Washington, D.C., the Purdue Research Foundation, West Lafayette, Indiana, and the Richard D. Irwin Foundation, Homewood, Illinois.     

Optimal Loan Interest Rate Contract Design

This paper analyzes optimal loan interest rate contracts under conditions of risky, symmetric information for one-period (static) and multi-period (dynamic) models. The optimal loan interest rate depends upon the volatility of, and co-variation among the market interest rate, borrower collateral, and borrower income, as well as the time horizon and the risk preferences of lenders and borrowers. For a risk-averse borrower with stochastic collateral, variable interest rate contracts are, in general, Pareto optimal. For plausible assumptions, the optimal loan interest rate for the multi-period model often exhibits muted responses to changes in market interest rates, making fixed rate loans a reasonable approximation for the optimal loan. Hence, in the absence of optimal contracts, long-term (short-term) borrowers tend to prefer fixed rate (variable) contracts.     

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.     

Dynamic portfolio choice with deferred annuities

We derive the optimal life-cycle portfolio choice and consumption pattern for households facing uncertain labor income, risky capital market, and mortality risk. In addition to stocks and bonds, the households have access to deferred annuities. Deferred payout life annuities are financial contracts providing life-long income to the annuitant after a specified period of time conditional on survival. We find that deferred annuities play an important role in household portfolios and generate significant welfare gains. Households with high benefits from state pensions, moderate risk aversion and moderate labor income risk purchase deferred annuities from age 40 and gradually increase their portfolio share. At retirement, deferred annuities account for 78% of total financial wealth. Households with low state pensions and high labor income risk purchase more annuities and earlier. Uncertainty with respect to future mortality rates has the same effect, i.e. household hedge against longevity risks using deferred annuities.