Borrower Credit and the Valuation of Mortgage-Backed Securities

We study the valuation of mortgage-backed securities when borrowers may have to refinance at premium rates because of their credit. The optimal refinancing strategy often results in prepayment being delayed significantly relative to traditional models. Furthermore, mortgage values can exceed par by much more than the cost of refinancing. Applying the model to an extensive sample of mortgage-backed security prices, we find that the implied credit spreads that match these prices closely parallel borrowers' actual spreads at the origination of the mortgage. These results suggest that models that incorporate borrower credit into the analysis may provide a promising alternative to the reduced-form prepayment models widely used in practice.     

UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation

We use a mean-reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lender's coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lender's (residual) exposure to house price risk, given the borrower's options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages.     

Pricing Default Risk in Mortgages

This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment. Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions. The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined. The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper.     

Savings and Loan Demand for Liquid Assets: Theory,Evidence and Implications for Policy*

In this study a model of liquid asset management for individual savings and loan associations is developed. The model combines features of portfolio theory and inventory theory and is used to draw hypotheses on the relationship between the demand for excess liquidity and a variety of independent variables. Pooled cross section-time series equations are estimated for the demand for excess liquidity of 198 S & Ls over the period 1974–1978. In addition to conclusions on the role of individual variables, the estimated equations reveal that the FHLBB can affect the portfolios of some, but not all, S & Ls. This implies that FHLBB liquidity policy can have an effect on the mortgage market.     

Valuing the Defeasance Option in Securitized Commercial Mortgages

To protect the interests of investors, commercial mortgage loans pooled for the issuance of commercial mortgage-backed securities (CMBS) have restrictive covenants that discourage the borrower from refinancing. Such restrictions limit the borrower's ability to access any accumulated equity. The predominant means of accessing this equity today is defeasance. By defeasing a loan, the borrower substitutes the commercial mortgage with U.S. Treasury or agency obligations whose payments match those of the defeased mortgage. Therefore, defeasance is an exchange option whereby the borrower gives up the portfolio of Treasury or agency securities and in return receives the market value of the commercial mortgage plus the liquidity benefits arising from accessing the accumulated equity in the underlying property. The value of the option to defease is shown to depend critically on the rate of return that can be earned on the released equity, prevailing interest rate conditions, as well as the option's contractual features.     

Strategic planning: valuing and managing portfolios of real options

This article presents a value-based strategic planning framework suitable for valuing and managing portfolios of corporate real options. The proposed framework combines insights from strategic management theory with novel quantitative valuation tools from finance. Strategic planning is viewed as a process of actively developing and managing portfolios of corporate real options in the context of competitive interactions. As such, the expanded valuation framework recognizes that future growth opportunity value deriving from the firm's resources and capabilities must explicitly account for uncertainty, adaptability, and competitive responsiveness. The resulting expanded valuation framework is able to capture the value of the adaptive resources and capabilities that enable a firm to adapt and re-deploy assets, develop and exploit synergies, and gain competitive advantage via time-to-market and first- or second-mover advantages. We show how two basic metrics in this value-based framework, current profitability of assets in place and future growth option value, can be obtained from financial market data and how they can be used in active portfolio planning.     

A Closed-Form,After-Tax,Net Present Value Solution to the Mortgage Refinancing Decision

Refinancing one's mortgage is often an attractive, wealth-enhancing option for homeowners in a declining mortgage rate environment. In some respects the decision is simple to analyze because future cash flows are relatively easy to define for fixed-rate mortgages. In other respects, however, the decision is nuanced by option pricing and tax considerations. The analysis must first begin with accurate after-tax, net present value solutions for varying potential holding periods. This study improves upon previous studies, which either ignore tax implications or address them iteratively in spreadsheet model solutions, by introducing a closed-form model that incorporates the ever-changing tax shield of the interest portion of each mortgage payment. Further, unlike many previous studies, our model does not assume that the current and replacement mortgages have equal remaining terms.     

How Subprime Borrowers and Mortgage Brokers Shared the Pie

We develop an equilibrium model for origination fees charged by mortgage brokers and show how the equilibrium fee distribution depends on borrowers' valuation for their loans and their information about fees. We use noncrossing quantile regressions and data from a large subprime lender to estimate conditional fee distributions. Given the fee distribution, we identify the distributions of borrower valuations and informedness. The level of informedness is higher for larger loans and in better educated neighborhoods. We quantify the fraction of the surplus from the mortgage that goes to the broker, and how it decreases as the borrower becomes more informed.     

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.     

Automated Underwriting and the Profitability of Mortgage Securitization

This paper develops a game-theoretic model of mortgage securitization, which is then used to examine a potential effect of automated underwriting. The paper's primary supposition is that automated underwriting lowers the costs to competitive mortgage originators and a monopolist securitizer of identifying mortgage applicants who are good credit risks. Faced with lower underwriting costs, originators will screen a larger number of mortgage applicants in the hopes of holding more good risks in their portfolios and passing through more bad risks to the securitizer. This mounting adverse-selection problem causes the securitizer's expected revenues to decline; this effect can outweigh the cost-saving benefit of automated underwriting, causing the securitizer's return on equity to fall.     

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.     

Relocation Opportunities and Mortgage Default

This paper presents a theoretical model of residential mortgage default when borrowers face beneficial as well as costly relocation opportunities. It amplifies and extends previous work by providing explicit conditions leading to default. The model also establishes when a borrower's relocation decision and default decision are dependent and when they are not.
A central result is that there is a range of book equity wherein the decision to default is not determined solely by the current level of equity or the borrower's ability to continue the mortgage payments. Rather, various costs and benefits, both tangible and intangible, enter into the decision. Specific conditions are identified that lead to relocation without default, default and relocation, and no default or relocation. The effects of changes in the variables upon default probability are presented.
Assuming that the borrower does not wish to retain ownership in the property, the model also predicts whether an individual borrower will choose prepayment or default when a relocation is made. The choice depends on the value of the relocation opportunity faced by the borrower, as well as financial variables such as house value, mortgage balance, and transaction costs. This finding suggests that existing empirical analyses of default may have omitted explanatory variables.     

Hedging Forward Mortgage Loan Commitments: The Option of Futures and a Future for Options

The purpose of this paper is to analyze theoretically the problem of how mortgage lending institutions assume the interest rate risks inherent in the granting of fixed-rate mortgage loan commitments.
Two approaches to hedge this risk are analyzed. First, the use of the GNMA futures market is evaluated from the standpoint of how it might be used to hedge against mortgage commitment risks. Secondly, the use of an appropriate pricing model—the Black-Scholes option pricing model—is offered as a proxy for establishing the market value of a fixed-rate mortgage commitment. This model is extended and empirically estimated for several hypothetical environments.
The paper demonstrates a basic flaw in the GNMA futures market as a hedge against mortgage commitments. Once this is established, the use of the options pricing approach is offered as a more rational approach for hedging these risks.     

Household Interest Rate Risk Management

I investigate household interest rate risk management by solving a life‐cycle asset allocation model that includes mortgage and bond portfolio choice. I find that most investors prefer an adjustable‐rate mortgage and thereby save on the bond risk premium that is contained in fixed‐rate mortgage payments. Only older, risk‐averse investors hold some fixed‐rate mortgage debt. Together with a position in short‐term bonds this enables them to hedge against changes in the real interest rate, while the inflation exposure of the debt and bond positions cancel out. Hedging house price changes with bonds only occurs at the end of the life cycle. Early in the life cycle short‐sale constraints prevent an effective hedge.     

Do Riskier Borrowers Borrow More?

Conventional wisdom in the mortgage industry holds that loan-to-value (LTV) ratios are positively correlated with mortgage default rates. However, not all empirical studies of mortgage loan performance support this view. This paper offers a theoretical signaling model of why the correlation between LTV ratios and default risk is contingent upon the default costs of the borrower. Specifically, the model proposes that when default costs are high there exists a separating equilibrium in which risky borrowers will self-select into lower LTV loans to reduce the probability of facing a costly default, while safe borrowers will self-select into higher LTV loans as a signal of their enhanced creditworthiness. This adverse selection process gives rise to the possibility of higher default probabilities for lower LTV loans. Conversely, when default costs are low the conventional result, in which risky borrowers select higher LTV loans than safe borrowers, is obtained. Empirical results, based on a sample of 859 single-family residential mortgage loans drawn from the portfolio of a national mortgage lender, are consistent with the separating equilibria predicted by the model.     

Reverse Mortgages and Interest Rate Risk

We develop and apply a valuation model that quantifies the interest rate risk inherent in fixed-rate reverse mortgages. Consistent with intuition, our results show that the interest rate risk of a reverse mortgage is greater than that of either a typical coupon bond or a regular mortgage. Somewhat surprisingly, we find that this difference in interest rate risk is extremely large. In fact, the interest rate risk of a reverse mortgage often is several orders of magnitude greater than the interest rate risk of other fixed-income securities.     

Estimating Borrower Mobility from Observed Prepayments

This article describes a method used to estimate parameters describing the mobility of borrowers choosing fixed-rate mortgages. Using a mortgage valuation model that predicts prepayments contingent upon parameters describing the distribution of expected tenure in the home, the average mobility of borrowers can be estimated from observed prepayment behavior. This article estimates the mobility of borrowers who chose fixed-rate mortgages before 1980 and borrowers who chose similar mortgages in the second half of the 1980s, when adjustable-rate mortgages were widely available. The empirical results support the claim that the average mobility of fixed-rate borrowers has declined.     

Prepayment Behavior of Dutch Mortgagors: An Empirical Analysis

The suboptimal exercise of the prepayment option in a mortgage is relevant for mortgage pricing and the management of a mortgage portfolio. Construction of an accurate prepayment model requires quantification of driving factors such as seasoning, seasonality, refinance incentive and burnout. We focus on Dutch mortgages but also discuss the Dutch market in a European setting. Within the euro-denominated MBS market, the Dutch market is often referred to as the benchmark market. In our application we include typical Dutch market and contract characteristics such as the annual penalty-free prepayment of 10 to 20% of the original loan amount. We use loan-level historical data on mortgages originated between January 1989 and June 1999 to estimate separate models for two popular redemption types: savings mortgages and interest-only mortgages. In both models we allow for suboptimal prepayment behavior. The results clearly indicate that prepayment rates depend on interest rates and the age of the mortgage contract. Moreover, we find that burnout is an important element in describing the prepayment behavior of Dutch mortgagors.     

A Simulation Approach to the Appraisal of Income Producing Real Estate

The income approach to appraising real property has been criticized in at least three general areas: the use of point estimates for input variables and market value, the failure to use an after-tax valuation model, and the ability of a single valuation model to capture the market for a given property. The objectives of this study are the development of an analytical framework and computer model to overcome these criticisms. The computer model is developed using Monte Carlo simulation and allows the appraiser to consider uncertainty, after-tax cash flows and numerous valuation models. The ability of appraisers to generate the necessary inputs and the interpretation of the output from the model are demonstrated using a case study.     

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.