Rational Prepayments and the Valuation of Collateralized Mortgage Obligations

This article presents a procedure for evaluating collateralized mortgage obligation (CMO) tranches. The solution procedure is in the spirit of a dynamic programming problem in which an individual mortgagor's decision to prepay is the feedback control variable―the mortgagor seeks to minimize the value of the mortgage subject to refinancing costs. We employ a two-step procedure to solve this dynamic programming problem. The first step uses an implicit finite difference backward solution procedure to determine the “optimal” prepayment boundary for a class of mortgagors, each of whom confronts the same proportional refinancing cost. This step is repeated for several different classes of mortgagors that differ in the level of refinancing costs that they confront. The outcome of this first step is a series of prepayment boundaries―one set of boundaries for each level of refinancing costs (i.e., one set of boundaries for each refinancing cost category of mortgagors). In the second step, the prepayment boundaries determined in the first step are used in conjunction with Monte Carlo simulation to value the CMO tranches. The essence of the second step is that when the simulated interest rate hits the boundary for a particular class, it triggers a prepayment scenario for that class of mortgagors. We conduct extensive sensitivity analysis to determine the robustness of this approach (and our solution procedure) to alternative single-factor models of the term structure of interest rates and to alternative specifications of the distribution of refinancing cost levels confronted by mortgagors. The sensitivity analysis indicates that CMO tranche valuation is not particularly sensitive to alternative models of the term structure so long as the models are consistent with the current yield curve, but, even when alternative specifications of the refinancing cost categories generate nearly identical values for the collateral underlying the CMO (i.e., the generic mortgage-backed securities), the resulting tranche values can differ widely between the two specifications. The results point out the importance of accurate estimation of the distribution of refinancing costs when the rational valuation model is used for the analysis of CMO tranches.     

Mortgage Refinancing Activity: An Explanation [1990–2001]

Mortgage refinancing activity reached unprecedented high levels during 1990–2001. Using GARCH to control for heteroskedasticity and separating the data into regimes to control for potential structural changes over time, we estimate a model explaining changes in mortgage refinancing activity over the period studied. We find changes in refinancing activity to be negatively related to current as well as past changes in the 30-year mortgage rate with a declining significant lag over time. Similarly, there is a significant lagged dependent variable with a declining lag. Moreover, mortgage refinancing activity is a substitute for other investments during certain regimes. These results offer evidence that home owners cash out the mortgage for other investments. The lags suggest that the process is delayed for a variety of reasons. The declining lag signals a faster response by consumers. The reasons for a faster response include a consumer perception that interest rates have “bottomed out,” the presence of an increase in consumer sophistication, and improvements in technology and market coordination that facilitate and reduce the cost of the refinancing process.     

Rational prepayment and the valuation of mortgage-backed securities

This article presents a new model of mortgage prepayments, basedon rational decisions by mortgage holders. These mortgage holdersface heterogeneous transaction costs, which are explicitly modeled.The model is estimated using a version of Hansen's (1982) generalizedmethod of moments, and is shown to capture many of the empiricalfeatures of mortgage prepayment. Estimation results indicatethat mortgage holders act as though they face transaction coststhat far exceed the explicit costs usually incurred on refinancing.They also wait an average of more than a year before refinancing,even when it is optimal to do so. The model fits observed prepaymentbehavior as well as the recent empirical model of Schwartz andTorous (1989). Implications for pricing mortgage-backed securitiesare discussed.     

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.     

The refinancing threshold pricing model: An economic approach to valuing MBS

Investigation of MBS prepayment data indicates that mortgagors have different interest rate levels, or thresholds, at which they exercise their option to prepay their mortgage. In order to properly value an MBS with heterogeneous mortgagors, Merrill Lynch has developed the Refinancing Threshold Pricing Model (RTP). The RTP model focuses on the refinancing decision of the mortgagor when pricing the mortgage pool. The model divides each pool into groups of mortgagors who share similar refinancing costs. Using market data, the RTP model endogenously determines both the implied costs that mortgagors face, as well as the proportion of the MBS pool in each refinancing cost group. In addition to determining pool value, the RTP model also calculates MBS duration, dP/dY and convexity. Comparison between RTP model values and actual market data reveals a strong correlation. The RTP has a wide range of applications, including valuing 15-year and 30-year conventional MBS; pricing interest-only (IO)/principal-only (PO) derivative MBS; determining new versus seasoned MBS price spreads; and valuing specific MBS pools.The information set forth was obtained from sources we believe reliable, but we do not guarantee its accuracy. Neither the information, nor any opinion expressed constitutes a solicitation by us for the purchase or sale of any securities or commodities. Merrill Lynch, Pierce, Fenner & Smith, Inc. or its affiliates may have either a long or short position in, and may buy and sell for its own account or the accounts of others, these securities.     

Houses as ATMs: Mortgage Refinancing and Macroeconomic Uncertainty

Mortgage refinancing activity associated with extraction of home equity contains a strongly countercyclical component consistent with household demand for liquidity. We estimate a structural model of liquidity management featuring countercyclical idiosyncratic labor income uncertainty, long- and short-term mortgages, and realistic borrowing constraints. We empirically evaluate its predictions for households' choices of leverage, liquid assets, and mortgage refinancing using microlevel data. Taking the observed historical paths of house prices, aggregate income, and interest rates as given, the model accounts for many salient features in the evolution of balance sheets and consumption in the cross-section of households over 2001 to 2012.     

Mortgage Brokers and the Refinancing Transaction: Evidence from CRA Borrowers

This study adds to an emerging literature on the lending practices of mortgage brokers during the run-up in home prices prior to 2006. Following a sample of low— and moderate-income borrowers through the first years following home purchase, the analysis identifies differences in the refinancing transaction associated with the use of mortgage brokers vs. retail lenders. Specifically, the analysis includes measures of the refinancing process, including whether the lender initiated contact with the borrower, whether the terms of the mortgage changed at closing, and the level of borrower satisfaction in hindsight. Care must be taken in extrapolating from this sample to the broader mortgage market, as all borrowers refinanced out of 30-year fixed-rate purchase mortgages in the Community Advantage Program (CAP). Nevertheless, analysis of this sample offers unique insight into borrowers’ interactions with mortgage brokers during the refinancing transaction. Origination with a mortgage broker, compared with origination through a retail lender, is associated with both a less satisfactory refinancing process and a higher likelihood of refinancing into an adjustable-rate mortgage (ARM).     

Interest-only and principal-only mortgage strips as interest-rate contingent claims

Interest-only (IO) and principal-only (PO) mortgage strips are valued in a stochastic interest-rate environment. The prepayment rate of the underlying mortgages is affected by two considerations not present in the pure financially rational model: (1) The property owner's holding period is assumed to follow a Gamma distribution, resulting in the possibility of prepayment due to the sale of the property (i.e., prepayment that is too early based on market interest rates); and (2) borrowers are assumed to face heterogeneous transaction costs related to refinancing the existing mortgage, and delay refinancing when market conditions make it optimal to do so (refinancing too late). Properties of IO/PO strips are identified by the finite difference method.     

Subprime Lenders and Mortgage Market Completion

Without a subprime market, some borrowers by virtue of poor credit history, unstable income, and other characteristics are unable to qualify for a mortgage. With a subprime market, there is a more complete credit supply schedule with the market pricing for poorer credit quality in the mortgage rate. By completing the capital market, subprime lenders reduce borrowing constraints. The result is a social welfare gain. Low-credit applicants otherwise denied funding are able to qualify by paying higher interest rates in exchange for offering more equity or lower loan-to-value ratios. This prediction is consistent with the subprime applicants financing or refinancing their mortgages at relatively low loan-to-value ratios.     

A Model of Mortgage Default

In this paper, we solve a dynamic model of households' mortgage decisions incorporating labor income, house price, inflation, and interest rate risk. Using a zero‐profit condition for mortgage lenders, we solve for equilibrium mortgage rates given borrower characteristics and optimal decisions. The model quantifies the effects of adjustable versus fixed mortgage rates, loan‐to‐value ratios, and mortgage affordability measures on mortgage premia and default. Mortgage selection by heterogeneous borrowers helps explain the higher default rates on adjustable‐rate mortgages during the recent U.S. housing downturn, and the variation in mortgage premia with the level of interest rates.     

Optimal dividend control for a generalized risk model with investment incomes and debit interest

This paper investigates dividend optimization of an insurance corporation under a more realistic model, which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive reserve and debit interest for negative reserve. Ruin occurs when the reserve drops below the critical value. The company controls the dividend pay-out dynamically with the objective to maximize the expected total discounted dividends until ruin. We show that the optimal strategy, is a band strategy and it is optimal to pay no dividends when the reserve is negative.     

No Job,No Money,No Refi: Frictions to Refinancing in a Recession

We study how employment documentation requirements and out-of-pocket closing costs constrain mortgage refinancing. These frictions, which bind most severely during recessions, may significantly inhibit monetary policy pass-through. To study their effects on refinancing, we exploit a Federal Housing Administration policy change that excluded unemployed borrowers from refinancing and increased others' out-of-pocket costs substantially. These changes dramatically reduced refinancing rates, particularly among the likely unemployed and those facing new out-of-pocket costs. Our results imply that unemployed and liquidity-constrained borrowers have a high latent demand for refinancing. Cyclical variation in these factors may therefore affect both the aggregate and distributional consequences of monetary policy.     

Optimal Mortgage Refinancing: A Closed‐Form Solution

We derive the first closed‐form optimal refinancing rule: refinance when the current mortgage interest rate falls below the original rate by at least In this formula W(.) is (the principal branch of) the Lambert W‐function, where ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, is the ratio of the tax‐adjusted refinancing cost and the remaining mortgage value, and τ is the marginal tax rate. This expression is derived by solving a tractable class of refinancing problems. Our quantitative results closely match those reported by researchers using numerical methods.     

Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.     

Interest Tax Shields: A Barrier Options Approach

There is a link between barrier options and tax shields of interest expense. We combine this link with a traditional valuation approach, to present practical valuation formulas for interest tax shields in three debt scenarios with risk of default: (1) constant debt, (2) delayed debt, and (3) debt refinancing. In all cases, default and refinancing are contingent on the random evolution of the income of the firm. For each scenario, we work out sensitivity analysis of the value of tax shields with respect to income, growth, systematic and business risk, risk-free interest rate, interest coverage ratio covenant, and the firm??s refinancing strategy.     

Interest rate risk and optimal design of mortgage instruments

This article develops and analyzes a simple expected utility model for interest rate risk and mortgage choice. The model demonstrates how the risks of interest rate changes should be allocated between borrowers and lenders through varying mortgage payments. In general, we conclude that full protection against interest rate risk, as a normative guideline, is likely to be suboptimal for the typical household. Our results show that the optimal design of adjustable rate mortgages should include an interest rate CAP provision.An earlier version of this article was presented at the American Real Estate and Urban Economics Association Meetings, Atlanta, Georgia, December 27–30, 1989.     

The demand for home mortgage assets by savings and loan associations

The purpose of this article is to analyze empirically the factors that enabled S&Ls to respond, concerning their demand for home mortgage assets, to the record high interest rates, inverted yield curves, and new competition for deposits by money market mutual funds. These factors include changing regulatory accounting procedures, increased participation in the secondary mortgage market, and increased asset diversification allowed for by Garn-St. Germain. The empirical results are based on a model of the demand for home mortgage assets specified in terms of an optimal marginal portfolio adjustment model. The results show that changing regulatory procedures and the subsequent impact on secondary mortgage markets had the most impact. The increased lending power granted by Garn-St. Germain had little effect on the demand for home mortgage assets by S&Ls.     

Systematic mistakes in the mortgage market and lack of financial sophistication

Institutions often offer a menu of contracts to consumers in an attempt to create a separating equilibrium that reveals borrower types and provides better pricing. We test the effectiveness of a specific set of contracts in the mortgage market: mortgage points. Points allow borrowers to exchange an upfront amount for a decrease in the mortgage rate. We document that, on average, points takers lose about $700. Also, points takers are less financially savvy (less educated, older), and they make mistakes on other dimensions (e.g., inefficiently refinancing their mortgages). Overall, our results show that borrowers overestimate how long they will stay with the mortgage.     

External shocks and the non-linear dynamics of Brady bond spreads in a regime-switching VAR

This paper analyzes the response of interest rate differentials between yields on Brady bonds and risk-less bonds to shocks in US interest rates and to conditions in global emerging bond markets. The effect of those shocks is likely to be non-linear. To capture this non-linear propagation, the reaction of refinancing conditions to shocks is investigated within a Markov-switching VAR framework that endogenously separates a crisis regime from a no-crisis regime. Regime-dependent impulse response functions reveal the non-linear response to external shocks. In periods of financial turbulences the positive impact of US rates breaks down. Likewise, shocks to other emerging markets are contagious in the sense that their negative impact is much more pronounced during times of financial distress.     

Competing Risks of Mortgage Termination: Who Refinances,Who Moves,and Who Defaults?

The Journal of Real Estate Finance and Economics - Why, when, and who terminates their mortgages? The primary reasons for mortgage termination are refinancing, selling of the property, and default....