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.     

Elective Mortgage Prepayment: Termination and Curtailment

Mortgage-prepayment risk underlies the structuring of mortgage-backed derivative securities, such as tranched real estate mortgage investment conduits. This prepayment comes either from mortgage termination or from curtailment, where the borrower retains the existing mortgage and prepays a portion. There are differences in cash flows from the two types of prepayment. In termination, the loan disappears from a pool, and the scheduled payment to investors in the pool is reduced. In curtailment, the loan survives, and the scheduled payment is unchanged but the term is reduced. There are implications for structuring mortgages and derivative securities. The prepayment decision is embedded in an in-tertemporal household utility maximization framework where choices are made between refinancing, making the regular payment, default or curtailment. Empirical results are presented for Government National Mortgage Association (GNMA) pools, and an algorithm is presented that separates the termination and curtailment components, facilitating the development of derivative securities.     

Movers and Shuckers: Interdependent Prepayment Decisions

We model competing risks of mortgage termination where the borrower faces a repeated choice to continue to pay, refinance the loan, move or default. Most previous empirical work on mortgage prepayment has ignored the distinction between prepayments triggered by refinancing and moving, combining them into a single prepayment rate. We show that financial considerations are the primary drivers of the refinance choice while homeowner characteristics have more influence on the move decision. We demonstrate that these differences are statistically significant and that combining these two distinct choices into a single measure of prepayment shifts coefficients toward zero and produces inaccurate predictions of aggregate termination rates. For example, a combined model underestimates the effect of the market price of the loan on refinancing; it misses entirely the opposite effects of borrower income on moving and refinancing. Our results suggest that existing prepayment models are inconsistent predictors of mobility-driven prepayment and underestimate the effect of market conditions and borrower characteristics on refinancing and housing decisions. Our findings have great significance to mortgage investors because mobility-driven prepayments are likely to be a more significant source of prepayments in thenext decade.     

An Arbitrage-Free Estimate of Prepayment Option Prices in Fixed-Rate GNMA Mortgage-Backed Securities

In an efficient market, the no-arbitrage condition implies that the price difference between any two assets must be the market value of all differences in their cash flows. We use this logic to deduce the price of the prepayment option embedded in fixed-rate Government National Mortgage Association (GNMA) mortgage-backed securities. The option price equals the difference between an observed GNMA price and the cost of a synthetic, nonprepayable GNMA constructed from the least expensive portfolio of Treasury securities that exactly replicates the promised GNMA cash flow stream, assuming prepayment is precluded. We regress the option prices on variables found significant in previous prepayment studies, finding that five key regressors explain more than 90% of the prepayment option value in pooled time-series cross-sectional analysis. We also show that the time value of the prepayment option calculated by our method displays a pattern similar to that produced by the Black-Scholes (1973) option pricing model. An additional empirical result is the existence of negative option prices and negative time value of the option prices. We attribute these to the fact that homeowners sometimes exercise their prepayment options when they are out-of-the-money, and to refinancing transaction costs. Our method is independent of assumptions regarding interest rate processes and the homeowner's prepayment behavior, and it provides a benchmark for testing theoretical prepayment models.     

Parameter Stability and the Valuation of Mortgages and Mortgage‐Backed Securities

The recent financial crisis was triggered by large and unexpected losses on mortgages and mortgage‐related securities. Here we examine model risk arising from innovations in mortgage markets and the effect on asset values. In particular, we examine the effect of parameter instability in the prepayment function. Using carefully constructed microdata, we find that the refinancing propensity was greater in 1998 for a 1997 issue given the same incentives, compared to the 1993 performance of a 1992 issue. The associated change in cash flow patterns produces economically significant changes in asset prices. Results are robust to alternative term structure models.     

An Empirical Test of a Two‐Factor Mortgage Valuation Model: How Much Do House Prices Matter?

This article develops a two-factor structural mortgage pricing model in which rational mortgage-holders choose when to prepay and default in response to changes in both interest rates and house prices. We estimate the model using comprehensive data on the pool-level termination rates for Freddie Mac Participation Certificates issued between 1991 and 2002. The model exhibits a statistically and economically significant improvement over the nested one-factor (interest-rate only) model in its ability to match historical prepayment data. Moreover, the two-factor model produces origination prices that are significantly closer to those quoted in the to-be-announced market than the one-factor model. Our results have important implications for hedging mortgage-backed securities.     

Mortgage Choice: What's the Point?

This article shows that, in the presence of transaction costs payable by borrowers on refinancing, it is possible to construct a separating equilibrium in which borrowers with differing mobility select fixed rate mortgages (FRMs) with different combinations of coupon rate and points. We also show that, in the absence of such costs, no such equilibrium is possible. This provides a possible explanation for the large menus of FRMs typically encountered by potential borrowers, and suggests that the menu available at the time of origination should be an important predictor of future prepayment. We numerically implement the model, developing the first contingent claims mortgage valuation algorithm that can quantify the effect of self-selection on real contracts in a realistic interest rate setting. The algorithm allows investors to account for self-selection when valuing mortgages and mortgage-backed securities. It also, for the first time, allows lenders to determine the optimal points/coupon rate schedule to offer to a specified set of potential borrowers, given the current level of interest rates.     

Fixed Come Hell or High Water? Selection and Prepayment of Fixed‐Rate Mortgages Outside the United States

We examine the decision to prepay a fixed‐rate mortgage in the United Kingdom, Canada, Ireland, Australia and New Zealand. These countries are characterized by having substantial fees which are associated with breaking a fixed‐rate mortgage. We develop a model which allows for fluctuations both in banks’ wholesale rates and credit spreads. We find that households can achieve economically significant benefits both from following an optimal prepayment strategy contingent on the break fee used by their bank and also by selection of fixed interest rate term and (where available) break fee structure.     

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.     

The Effect of Refinancing Costs and Market Imperfections on the Optimal Call Strategy and the Pricing of Debt Contracts

This article, which was originally written in 1986, develops a methodology for valuing mortgage-backed securities with refinancing costs. We solve simultaneously for the valuation of the mortgage-backed security (loan) and the borrower's refinancing strategy, pricing all coupon levels simultaneously. Because the borrower may refinance his or her loan and incur costs at many times in the future, the optimal refinancing decisions arise from an optimal dynamic strategy that reflects the costs of all potential future refinancings. Though the borrower faces multiple rounds of refinancing costs, the market value of the loan cannot exceed the call price plus a single round of refinancing costs.     

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.     

Lenders’ pricing strategy: Do neighborhood risks matter?

This article explores the different pricing strategies of lenders who originate both government-sponsored enterprise (GSE) and non-GSE loans. We find that conditional on loan and borrower characteristics and some observable local economic factors, mortgage rates on GSE loans vary significantly across regions. However, we observe no sizable regional variation in loan amounts or default risk. By contrast, the mortgage rates on non-GSE loans depend almost entirely on borrowers and loan characteristics. In addition, we find that spatial variations in GSE mortgage rates are highly responsive to regional prepayment risk. Our results are robust to various controls for neighborhood characteristics, including regional-level bank competition, borrower accessibility to mortgages, and household income levels. Overall, the findings offer a novel insight into how lenders adjust pricing strategies in response to a changing lending environment. The results provide implications relating to the present and imminent dangers of housing bubbles and the intensified refinancing wave following the COVID-19 pandemic.     

The Termination of Commercial Mortgage Contracts through Prepayment and Default: A Proportional Hazard Approach with Competing Risks

This article examines the factors driving the borrower's decision to terminate commercial mortgage contracts with the lender through either prepayment or default. Using loan–level data, we estimate prepayment and default functions in a proportional hazard framework with competing risks, allowing us to account for unobserved heterogeneity. Under a strict definition of mortgage default, we do not find evidence to support the existence of unobserved heterogeneity. However, when the definition of mortgage default is relaxed, we do find some evidence of two distinctive borrower groups. Our results suggest that the values of implicit put and call options drive default and prepayment actions in a nonlinear and interactive fashion. Prepayment and default risks are found to be convex in the intrinsic value of call and put options, respectively. Consistent with the joint nature of the two underlying options, high value of the put/call option is found to significantly reduce the call/put risk since the borrower forfeits both options by exercising one. Variables that proxy for cash flow and credit conditions as well as ex post bargaining powers are also found to have significant influence upon the borrower's mortgage termination decision.     

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.     

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.     

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.     

Determinants of Credit Spreads in Commercial Mortgages

This article examines the cross-sectional and time-series determinants of commercial mortgage credit spreads as well as the terms of the mortgages. Consistent with theory, our empirical evidence indicates that mortgages on property types that tend to be riskier and have greater investment flexibility exhibit higher spreads. The relationship between the loan-to-value (LTV) ratio and spreads is relatively weak, which is probably due to the endogeneity of the LTV choice. However, the average LTV ratio per lender has a strong positive relation with credit spreads, which is consistent with the idea that lenders specialize in mortgages with either high or low levels of risk, and that high LTV mortgages require substantially higher spreads. Finally, we observe that spreads widen and mortgage terms become stricter after periods of poor performance of the real estate markets and after periods of greater default rates of outstanding real estate loans.     

Mortgage Default and Prepayment Risks among Moderate‐ and Low‐Income Households

Using a unique sample of community reinvestment loans, we study the propensity of very low‐income households to terminate a mortgage and compare it to the outcomes for low‐income and moderate‐income households. The results indicate that, even within moderate‐ and low‐income segments, lower or very low income is associated with higher default and lower prepayment probabilities. In addition, depending on how low the borrower's income is, classic determinants of loan termination such as credit scores, the amount of equity in the home and local labor market conditions can have different impacts on default and prepayment probabilities.     

FHA Terminations: A Prelude to Rational Mortgage Pricing

Recent models of pricing mortgages and/or mortgage insurance have used option-pricing models as their framework. The focus is usually on default, which is viewed as a put option (to sell the house to the lender in exchange for the mortgage) and prepayment, which is viewed as a call option (to buy the mortgage from the lender). Analysis then uses techniques like those used to price options in capital markets. Unfortunately, homeowners do not seem to exercise their option as quickly as do traders in organized markets. We estimate prepayment and default functions, which are meant to be a first step in developing modified, option-based models of mortgage pricing.     

Mortgage Refinancing with Asymmetric Information

Information asymmetry exists between the lender and the borrower regarding the holding period of the mortgaged real estate; the lender does not know how long the borrower plans to own the house. This information asymmetry allows the cost of obtaining a mortgage to deviate from its value to the borrower. As a result, the exercise price of the option to refinance becomes the cost to the borrower of obtaining a new mortgage instead of the outstanding balance of the existing mortgage as used in previous models. The option to refinance is a sequential option; after the borrower refinances, a new option is obtained to refinance again in the future. A mortgage refinancing model is developed taking information asymmetry and sequential refinancing into account. The model is used to solve for (1) the value to the borrower of a callable mortgage and (2) the minimum interest rate differential between the contract rate of the existing mortgage and the market interest rate needed to justify refinancing.