Optimal Mortgage Refinancing with Stochastic Interest Rates

The purpose of this paper is to develop a dynamic model of mortgage refinancing in a contingent claim framework that simultaneously solves for the borrower's optimal mortgage refinancing strategy, the value of the refinancing call option, the value of the mortgage liability to the borrower, and the market (lender) value of the fixed-rate contract. We also calculate the minimum differential between the contract rate on the existing mortgage and the current interest rate that is required to trigger an optimal mortgage refinancing.     

Optimal Sharing of Interest‐Rate Risk in Mortgage Contracts: The Effects of Potential Prepayment and Default

Much of the literature on the economics of mortgage markets has studied the fixed vs. adjustable‐rate mortgage choice made by individual borrowers. However, to decide if the outcome of such a choice is efficient or approximately so, it is necessary to explore the question of optimal risk‐sharing in mortgage contracts. But because only a small literature has studied this question, more research is clearly warranted. The present article helps fill this gap by developing a simplified version of Arvan and Brueckner's model, using it to characterize optimal contracts in the absence of mortgage termination, and then exploring how termination via prepayment or default affects optimal risk‐sharing. The broad conclusion of the analysis is that potential mortgage termination makes higher risk exposure for borrowers optimal.     

A Simple Model of Mortgage Insurance

This paper uses a two-period model to analyze the borrower's choice of an optimal time pattern of mortgage payments in a world where future house values are uncertain. Since a decline in values can make the borrower's equity negative, leading to default on the mortgage, lenders in the model will require the purchase of mortgage insurance. The premium on the insurance policy will depend on the riskiness of the mortgage, which in turn depends on the magnitude of the initial mortgage payment. Mortgages with large (small) first payments will carry low (high) insurance premiums. Taking this fact into account, the borrower decides on the optimal riskiness of his mortgage. Borrowers who discount the future heavily choose risky mortgages carrying high insurance premiums, while those who place a higher value on future consumption opt for less risky contracts carrying low (or zero) premiums.     

Pricing Mortgage-Backed Securities: Integrating Optimal Call and Empirical Models of Prepayment

Residential mortgage borrowers frequently appear to behave suboptimally with respect to their mortgage prepayment options. Many borrowers fail to exercise even well-into-the-money options while others prepay when the call option is out-of-the-money. To account for these apparently suboptimal prepayments, the recent trend in mortgage-backed securities research has been away from optimal call valuation models, in which the decision to exercise is determined endoge-nously, in favor of models in which prepayment behavior is exogenously specified based on empirical estimation. This paper develops a rational model of mortgage prepayment which incorporates both types of "non-optimal" prepayment and retains endogenous call. This enables the model to disentangle and compare the separate effects of the interest rate call, impeded by transaction costs, and of non-interest-rate driven prepayment. In addition, by recognizing heterogenous borrower transaction costs, the model presents a way to account more precisely for the varying prepayment lags associated with well-into-the-money call options and to account for the phenomenon of "burnout" within a mortgage pool. The paper includes an empirical test of the unbiasedness of the integrated pricing model by comparing simulated prices from our theoretical model to observed prices on traded Fannie Mae and GNMA securities.     

Unobservable Risks in Mortgage Contract Choice

This study proposes a lifetime utility maximization model where borrowers choose optimal mortgage bundles including mortgage type, loan‐to‐value and loan size to maximize their allocation of limited budgets between housing and nonhousing consumptions. The model predicts that the mortgage bundle choices by borrowers of different income and risk attributes explain significant variations in the ex post default risks of the borrowers. The empirical tests using sampled mortgages pooled in nonagency residential mortgage backed securities support the hypothesis that the optimal choice of mortgage bundles reveals hidden risk factors of borrowers, which, if ignored, could lead to misjudgment of ex post default of borrowers.     

Throwing Good Money After Bad? Cash Infusions and Distressed Real Estate

When a leveraged real estate project experience cash-flow problems, the owner must either inject additional cash or default on the mortgage. We show that it is not optimal for the owner to default as soon as net cash flow becomes negative. Surprisingly, the owner can expropriate some of the mortgage lender's wealth by injecting cash and continuing to pay interest. When the owner has cash constraints, outside investors may be able to extract significant economic rents by financing distressed real estate projects. These results have interesting implications for mortgage lending and the pattern of real estate transaction volume.     

Commercial Mortgage Pricing with Unobservable Borrower Default Costs

This paper develops a pricing model for commercial real estate mortgage debt that recognizes the influence of default transaction costs on the borrower's default decision. These costs are heterogeneous across borrowers and largely un-observable to the lender/investor at the time of origination or loan purchase. A recognition of these unobservable costs can explain why borrower default decisions may differ from those predicted by "ruthless" mortgage-default pricing models. We address the determinants of default choice and timing by replacing sharp default boundaries found in the ruthless models with "fuzzy" boundaries that account for investor uncertainty with respect to evaluating borrower default decisions. To implement our model, we estimate probabilities of default as a junction of time and net equity in the property. Then, given that default occurs, loss severities are modeled based on expected property value recovery net of foreclosure costs and time until the asset is actually sold. Under reasonable parameter value choices, resulting Monte Carlo simulations produce numerical mortgage price estimates as well as component default frequency and severity levels that realistically reflect default premiums and loss levels observed in the marketplace.     

Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default

This article investigates the impact of spatially correlated unobservable variables on the refinancing, selling and default decisions of mortgage borrowers. Virtually the entire mortgage literature acknowledges that borrower-specific characteristics, such as culture, education or access to information, play an important role in mortgage termination decisions. While we do not observe these variables directly, we note that borrowers of similar background tend to cluster together in neighborhoods. We estimate a competing risks hazard model with random effects using a three-stage maximum likelihood estimation approach. We utilize the space-varying coefficient method to modify the covariance structure according to the spatial distribution of the observations. Beyond a significant improvement of the model performance, this yields a number of insightful implications for mortgage termination behavior. For instance, borrowers of the affluent "West Side" of Los Angeles County both refinance and move at a higher rate than predicted by the standard maximum likelihood estimation method. At the same time, borrowers from some lower-valued neighborhoods tend to stay longer than expected with their mortgages and properties.     

The Effect of Mortgage Payment Reduction on Default: Evidence from the Home Affordable Refinance Program

This article evaluates the effect of payment reduction on mortgage default within the context of the Home Affordable Refinance Program. We find that mortgage default is sensitive to payment reduction using univariate, duration and hazard modeling approaches. A relative risk Cox model of default with time‐varying covariates estimates that a 10% reduction in mortgage payment is associated with about a 10–11% reduction in monthly default hazard for loans. This finding is robust to the inclusion of empirically important mortgage risk drivers (such as current loan‐to‐value and FICO score) as well as controlling for selection effects based on observables.     

Housing Finance in a Stochastic Economy: Contract Pricing and Choice

An empirical analysis of macroeconomic time series from the mortgage, housing, capital and labor markets is based on life-cycle consumption and mortgage option pricing considerations. Vector autoregression techniques characterize the long-run equilibrium and short-run dynamics of the mortgage market as it relates to the other sectoral markets. A simultaneous-equations model characterizes the partial equilibrium in the differentiated products market for fixed- and adjustablerate mortgage contracts. The empirical results reveal the impacts that market conditions have on mortgage volumes and prices, and they generally support the implications of the consumption and pricing theories.     

Semivariance of Property Value Estimates as a Determinant of Default Risk

Standard practice in the residential mortgage underwriting industry is to estimate collateral values via independent appraisals conducted by third parties. This paper empirically examines the role of property value ( i.e. , appraisal) uncertainty as a determinant of default on residential mortgage loans. Based upon an analysis of 1,428 residential loans drawn from the portfolio of a national mortgage lender, we find evidence that semivariance in property value uncertainty is related to default risk. Specifically, subject properties that are valued above the sales price of recently sold "similar and proximate" properties show evidence of greater default risk. Interestingly, a variance (range) measure of property value uncertainty is not significantly related to default risk.     

Mortgage Shoppers: How Much Do They Save?

Survey evidence suggests that many U.S. and European consumers do not spend a lot of time comparing mortgage products. We show, however, that mortgage shopping is associated with a substantial monetary payoff, using a unique data set from a website where borrowers (not the lenders) can post their complete set of received mortgage rate offers. A borrower who shops for five mortgage offers is able to save 7,078 euros in net present value on average. The potential savings suggest suboptimal mortgage shopping as the opportunity cost of time to renegotiate additional quotes is unlikely to be that high.     

The Effects of Securitization on Mortgage Market Yields: A Cointegration Analysis

Securitization of the residential mortgage market has completely transformed the process of financing home loans in the U.S. over the last two decades. We examine the effects of securitization on yield spreads in the primary mortgage market. Cointegration techniques are employed to test the relationship between the increasing volume of mortgage securities over time and the yield spread on mortgage loan rates. We find that a 10% increase in the level of mortgage securitization as a proportion of total mortgage originations decreases yield spreads on home loans by as much as 20 basis points. Other results indicate that, while prepayment speed has a significant effect on mortgage yield spreads, default risk does not. We conclude that securitization of the residential mortgage market plays an important role in decreasing the cost of home loans.     

Interest Rate Risk, Residential Mortgages and Financial Futures Markets

Residential mortgage markets in both the United States and Canada have recently been dominated by instruments such as variable-rate and short-term rollover mortgages which require borrowers to assume a greater burden of interest rate risk. An outstanding question is whether this approach to risk allocation is Pareto optimal or whether there are other more effective methods of dealing with the risk created by interest rate volatility. This study examines the potential for shifting this risk from the mortgage market to the financial futures market. After considering the rationale for expecting that neither mortgage borrowers nor lenders wish to absorb the high levels of risk present in the existing financial environment, this study discusses the hedging of interest rate risk through financial futures markets. Empirical tests are then performed to evaluate the effectiveness of U.S. futures markets for hedging positions from the U.S. mortgage market. These results indicate that the interest rate risk inherent in residential mortgages can be substantially shifted through one or more positions in the existing futures contracts and long-term, fixed-rate mortgages may still be financially feasible under conditions of interest rate volatility.     

Reverse Mortgages: Contracting and Crossover Risk

A pricing model is developed for a reverse mortgage contract where the borrower receives payments either as a lump sum or in an annuity while the loan balance accumulates as a claim against the house. No underwriting criteria on income are applied. One risk of default is that the borrower will remain in the house after the negatively amortizing loan balance exceeds the value of the house. An explicit pricing model of the reverse mortgage permits the evaluation of this default "crossover" option. Alternative methods involving life insurance contracts and securitization are compared as secondary market channels.     

An Analysis of the Ex Ante Probabilities of Mortgage Prepayment and Default

Observed mortgage prepayment and default rates have been far different than the ruthless option exercise rates predicted by contingent claims models of mortgage pricing. The discrepancies have been attributed to both the competing-risk nature of prepayment and default and to transactions costs. This paper tries a different means of reconciliation. We introduce a third stochastic process, household income, into the usual pricing model that includes only the spot interest rate and the house price. The presence of income allows considering consumption-theoretic determinants of termination. The role of mortgage underwriting rules in restricting optimal prepayment is also explicitly modeled. Numerical ex ante prepayment and default rates based on the theoretical model come much closer to historical experience.     

Transaction Costs, Suboptimal Termination and Default Probabilities

The same option-based methodology now commonly used to value mortgages and their termination features also can be applied to calculate the probabilities that mortgage default will occur. This paper pursues that idea, and furthermore, enriches the idealized option-based approach by introducing both transaction costs and "suboptimal" termination. These latter features capture the individual considerations that cause a mortgage holder's actions to differ from what rationality would indicate based solely on the market value of the mortgage. These features are of considerable importance if the results of options-based models are to be made comparable to those calculations of default probabilities occurring in the empirical literature.     

Why Do We Have ARMs?

This paper suggests a resolution to the paradox of inefficient risk bearing by adjustable-rate mortgage (ARM) borrowers. The analysis shows that when contracts are written in a realistic way, with payments linked across time via a common loan-rate function, risk sharing and the tilt of the mortgage payment stream become inextricably linked. Unless time preferences are identical or the cost of funds exhibits no time trend, borrowers will accept interest-rate risk in order to gain a more favorable time path of mortgage payments.     

The Effects on Mortgage Repayments of Restrictions on the Enforcement of Due-on-Sale Clauses: The California Experience

Unexpected increases in the cost of mortgage funds have imposed substantial losses on mortgage lenders. The losses are compounded by the decline in mortgage repayments as homeowners hang on to their low-rate mortgages. The enforcement of due-on-sale clauses is one option lenders have had to inhibit reductions in the turnover of low-rate mortgages. Recently a California Supreme Court ruling restricted the use of due-on-sale clauses. As a result, California state-chartered associations can no longer use due-on-sale clauses to raise mortgage rates. At the same time, most federally chartered associations in California continued the unrestricted enforcement of due-on-sale clauses. This paper examines the behavior of repayment rates at restricted state and unrestricted federal associations in California. The results suggest that for each percentage point new mortgage interest rates exceeded rates on existing mortgages, repayment rates at federal associations declined by 1.532 percentage points. The inability to prevent mortgage assumptions caused repayment rates at state-chartered associations to fall 0.406 percentage points more than federal association repayment rates. The additional decline has added substantial income losses to California state associations.     

Mortgage Pass-Through Securities: Progress and Prospects

This paper discusses the Housing Commission's perspective and recommendations on mortgage pass-through securities markets, reviews federal policy toward such securities in the wake of the Housing Commission Report , and considers prospects for mortgage securities in the housing finance system of the future. Concerning the outlook, it is concluded that massive "securitization" of housing finance may not be inevitable–contrary to the developing conventional wisdom on this topic–partly because the underlying need for secondary market transactions may not be as strong as commonly expected. Furthermore, the relative importance of pass-through securities as secondary market vehicles may erode if federally related programs are phased down in line with Housing Commission recommendations, even if policies currently being developed within the Administration to improve the functioning of fully private securities markets are implemented.