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.     

Stochastic Modeling of Federal Housing Administration Home Equity Conversion Mortgages with Low-Cost Refinancing

Federal Housing Administration-insured reverse mortgages, known as Home Equity Conversion Mortgages (HECMs), did not originally have a provision for low-cost refinancing. If a borrower's house value increased faster than expected, the borrower could not tap that additional equity without terminating the first loan and originating a new HECM loan with full closing costs. We test several low-cost refinancing options using a stochastic simulation model that allows interest rates and house prices to vary in historically accurate patterns. Low-cost refinancing decreases the net value of the fund by 54% to $98.5 million, but it remains positive in 80% of the trials.     

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.     

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.     

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.     

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.     

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.     

Reverse Mortgages and Prepayment Risk

This paper presents a detailed assessment of the Connecticut Housing Finance Authority (CHFA) reverse annuity mortgage (RAM) program. Because of the size and payment history of the program, the analysis provides an empirical framework on which to develop and assess other home equity conversion (HEC) programs. The program offers insights into the economic impact of these programs and the factors affecting prepayment. The program issued 765 annuities over five years, and 240 of these loans have terminated payments. The annuity payments had a demonstrable financial impact on the elderly participants, with an 88% average annual income increase. Prepayment rates varied across borrower and loan characteristics. The rates were most sensitive to marital status and were heavily affected by the age of the borrower and the term of the loan. Although default risk exists, the evidence indicates a low probability of the loan value exceeding the house value.     

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.     

The HAMP NPV Model: Development and Early Performance

The foreclosure crisis that began in 2008 triggered the need for new approaches to treat distressed mortgages. A key component of the Obama Administration's Home Affordable Modification Program (HAMP) was the development of a standardized Net Present Value (NPV) Model to identify troubled loans that were value‐enhancing candidates for payment‐reducing modifications. This article discusses the development of the HAMP NPV Model, 1 its purpose and some important constraints that dictated its structure and limitations. We describe the structure and the estimation of the model in detail. We also describe the responsiveness of the model to key characteristics, such as loan‐to‐value and credit score, as well as provide new evidence on the relationship between HAMP modification performance and key borrower and modification characteristics. The article concludes with a discussion of model limitations and the future role of systematic loan modification using NPV analysis.     

The Impact of Interstate Foreclosure Cost Differences and the Value of Mortgages on Default Rates

Previous research on mortgage default has focused on the costs, benefits, and characteristics of the mortgagor. In such studies default rates have been taken as a measure of mortgage risk. In this paper we present a model where the position of the lender affects the default-foreclosure process. Important to the lender's decision to foreclose rather than renegotiate an existing loan are the value of mortgage and the legal costs associated with foreclosure.
The empirical evidence supports the hypothesis that both the value of the mortgage and legal foreclosure costs affect the foreclosure rate. In those states where legal foreclosure costs are high rates are significantly less than where costs are low. This suggests that previous models which include only the costs and benefits of default to the borrower are incomplete and that foreclosure rates can not be taken as a strict measure of mortgage risk. That is, low foreclosure rates may indicate that losses occur in other forms of loan negotiation rather than in expensive legal costs.     

The Impact of Homeowners' Housing Wealth Misestimation on Consumption and Saving Decisions

Using a unique data set of 81,943 house value estimates by the homeowners and their financial institution, I find that homeowners overestimate their house value by 3.1%. After controlling for homeowners' socioeconomic characteristics, I find that ex ante homeowners who rate (cash-out) refinance an existing loan to increase savings (consumption) are significantly more likely to underestimate (overestimate) their house value. Moreover, overestimators (underestimators) are more likely to increase (reduce) their spending ex post . Finally, I also find that underestimators are more likely to prepay their loans and overestimators are more likely to default on their loans.     

Loan Subsidy Valuation: An Alternative Approach

In a recent paper, Jennergren analyzed four loan subsidy valuation methods suggested in authoritative textbooks. He showed that the first three can be derived from a unique formula whose value depends on the nonsubsidized loan amount that is assumed to be replaced by the subsidized loan. When the WACC method is used, this debt replacement must implicitly take into account the target debt-to-value ratio set by the firm. In this article, we suggest an alternative approach that allows us to clearly incorporate the corresponding debt constraint and to determine the resulting adjustment to be made. This adjustment appears to be different from that recommended by Jennergren. More generally, we suggest an alternative view of the consistency of the methods.     

商品房按揭贷款与资金的时间价值

本论述了商品房按揭贷款中，置业应正确认识贷款本金的偿还是按复利计算时间价值的，正确对待贷款购房中的“杠杆作用”。为置业在住房贷款中，代款数额、贷款方式、还款时间、还款方式的确定提出合理建议。     

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.     

The Impact of Second Loans on Subprime Mortgage Defaults

An estimated 12.6% of primary mortgage loans were simultaneously originated with a second loan from 2004 until 2008, although relatively little is known about how the presence of such subordinate loans affects the default decisions of borrowers. We use a novel data series of loan servicing records from 2002 until 2010 to identify such borrowers and find evidence that the default behavior of these borrowers significantly differs from borrowers without second loans. Estimating a discrete‐time proportional odds hazard model, we find borrowers with a second loan were 62.7% more likely to default each month on their primary loan when conditioning alone on the attributes of the primary loan. However, borrowers of second loans were 58.3% less likely to default on their primary loan as compared to single‐loan borrowers with equivalent current combined attributes (i.e., loan‐to‐value, balance and interest rate). We hypothesize and provide empirical evidence that this occurs because borrowers with second loans have the option to sequentially default on each loan since subordinate lenders will not pursue foreclosure if borrowers have insufficient equity. Lenders of defaulted subordinate debt may revisit their decision to foreclose in the future after housing markets start to recover, thus prompting a new round of foreclosures.     

Lender Steering in Residential Mortgage Markets

In this article, we examine the incentives for lenders to steer borrowers into piggyback loan structures to circumvent regulations requiring primary mortgage insurance (PMI) for loans with loan‐to‐value ratios (LTV) above 80%. Our empirical analysis focuses on propensity score‐matched portfolios of piggyback and single‐lien loans having the same combined LTV based on a full set of observed risk characteristics. Our results confirm that mortgages originated with the piggyback structure have much lower ex post default rates and faster prepayment speeds than corresponding PMI loans. We also find a significant causal effect of interstate banking deregulation on the growth of piggybacks in these years, confirming that the ex post performance gap is primarily driven by lender steering on the supply side and not by borrower self‐selection. We then perform a number of tests to explore different origination and execution channels of mortgage steering.     

The Effects of Securitization on Consumer Mortgage Costs

We examine the effects of securitization on two dimensions of consumer mortgage costs: coupon rates and loan origination fees. We find no evidence that securitization reduces the coupon rates on fixed- or adjustable-rate mortgages. Instead, securitization appears to lower mortgage loan origination fees, resulting in substantial savings for consumers. Securitization activity includes passthrough creation and collateralized mortgage obligation (CMO) creation. We test for differences between the effects of passthrough and CMO creation on primary mortgage costs. Surprisingly, these activities appear to have indistinguishable effects on loan rates and origination fees, suggesting that a large derivatives market for mortgage loans is not creating value for consumers.     

工业集聚与污染排放强度——基于固定效应门限回归模型的再检验

为研究工业集聚对污染排放强度的影响,本文选取2000~2015年全国30个省市（自治区）的面板数据,以工业集聚为门槛变量,利用固定效应门限回归模型,实证分析了不同工业集聚水平对污染排放强度的影响。结果发现：工业集聚对废水排放强度的影响存在显著门槛效应,在达到门槛值前,工业集聚很大程度降低了废水排放强度,在跨过门槛值后,这种作用会减弱。工业集聚与废气排放强度呈显著倒“U”型关系,在工业集聚水平小于门槛值时,工业集聚会加剧废气排放,大于门槛值后,工业集聚会降低废气排放强度。工业集聚会降低废物排放强度,但未出现显著门槛效应。     

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.