Mortgage Contracts,Strategic Options and Stochastic Collateral

This paper offers a game-theoretic model for both the analysis and valuation of mortgage contracts in the context of an economy with complete information and complete contingent claims markets. We analyze the equilibrium strategy of the lender, who holds an option over the magnitude of mortgage credit extended per dollar of collateral offered, and the mortgagor, who holds options to default or prepay, in a class of intertemporal mortgage contracts collateralized by property evolving according to a random process which is common knowledge to both parties to the mortgage contract. Using continuous–time arbitrage valuation principles, we derive the value of the mortgage contract to both parties and show, through both analytical solutions and numerical simulations, that Markov perfect equilibria exist in which, among other properties, a lower flow of housing services accruing to the borrower, per dollar of initial house value, and a correspondingly lower rate of effective depreciation, will elicit a larger volume of funds offered by a lender; the amount of credit offered, the values of the contract to both lender and mortgagor, and the expected losses to both parties from costly bankruptcy are highly sensitive to the perceived volatility of the value of the property collateralizing the mortgage, even in an economy with complete markets or risk neutrality on the parts of lender and borrower; the upper limit on mortgage credit offered by a rational lender may be a small fraction of the current fair market value of the property, regardless of the contractual yield offered by the borrower, and will decrease, at each such yield, as bankruptcy costs or housing service flows increase; and under significant but plausible values for bankruptcy and costs of liquidating property under foreclosure, the flow of mortgage credit can become negatively related to the spread of the mortgage yield over the riskless rate, with the lender preferring a lower contractual yield to a higher one.     

Breakeven Determination of Loan Limits for Reverse Mortgages under Information Asymmetry

Since the loan limit of a reverse mortgage is a major concern for the borrower as well as the lender, this paper attempts to develop an option-based model to evaluate the loan limits of reverse mortgages. Our model can identify several crucial determinants for reverse mortgage loan limits, such as initial housing price, expected housing price growth, house price volatility, mortality distribution, and interest rates. We also pay special attention to the important implication of mortgage lenders’ informational advantage over reverse mortgage borrowers concerning housing market risk. In reverse mortgage markets, the elderly borrowers typically hold far less, relative to the lenders, or no information about the lenders’ underlying mortgage pools. Such information asymmetry leads these two categories of market participants to generate different perspectives on the risk of the collateralized properties, which can be identified to be important in determining the maximum loan amounts of reverse mortgages. We further find that the maximum loan amount of a reverse mortgage decreases in the correlation between the returns on the pooled underlying housing properties but increases with the number of the pooled mortgages.     

Residential Mortgage Default: The Roles of House Price Volatility, Euphoria and the Borrower’s Put Option

House price volatility; lender and borrower perception of price trends, loan and property features; and the borrower’s put option are integrated in a model of residential mortgage default. These dimensions of the default problem have, to our knowledge, not previously been considered altogether within the same investigation framework. We rely on a sample of individual mortgage loans for 20 counties in Florida, over the period 2001 through 2008, third quarter, with housing price performance obtained from repeat sales analysis of individual transactions. The results from the analysis strongly confirm the significance of the borrower’s put as an operative factor in default. At the same time, the results provide convincing evidence that the experience in Florida is in part driven by lenders and purchasers exhibiting euphoric behavior such that in markets with higher price appreciation there is a willingness to accept recent prior performance as an indicator of future risk. This connection illustrates a familiar moral hazard in the housing market due to the limited information about future prices.     

Determinants of the incidence of U.S. Mortgage Loan Modifications

This paper combines data on the performance of mortgage loans with detailed borrower, neighborhood, and property characteristics to examine the factors that determine the outcomes of seriously delinquent loans. We employ multinomial logit models in a hazard framework to explain how loan, borrower, property, servicer and neighborhood characteristics affect which of the following four outcomes results from a seriously delinquent loan: (1) the borrower cures the delinquency; (2) the borrower and lender agree to modify the loan; (3) the borrower suffers a liquidation (short sale, deed in lieu, foreclosure auction sale or REO); or (4) the loan remains delinquent. In particular, we focus on mortgage modification. We find that the outcomes of delinquent loans are significantly related to: current LTV, FICO scores, especially risky loan characteristics, the servicer of the loan, neighborhood housing price appreciation, and whether the borrower received foreclosure counseling.     

Do Savings Associations Have a Special Commitment to Housing?

In this paper, we investigate whether elimination of the savings association charter might reduce lending to nontraditional mortgage borrowers. We present a theoretical model of lender portfolio choice, in which nontraditional lenders have some market power and traditional lenders are price takers in the mortgage market. The comparative statics indicate differences between nontraditional and traditional lenders in terms of their asset allocation responses to changes in borrower income and house prices. Empirical tests indicate the absence of such differences between savings associations and commercial banks, suggesting that elimination of the savings association charter would not impair lending to nontraditional mortgage borrowers.     

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.     

Differences in the Cost of Mortgage Credit Implications for Discrimination

This paper estimates the mortgage interest rate differences paid by Asian, Hispanic, and African–American borrowers to a national home mortgage lender in the years 1988–1989. Controlling for differences in market rates, rate lock protection, and borrower risk factors, conventional loan interest rates are almost perfectly race-neutral. The single deviation from race-neutrality is that when interest rates fall during the borrower's rate-lock period, only African–American borrowers are unable to capture a share of this decline. Government (FHA and VA) credit models show small premia paid by African–American borrowers of about $1.80 per month on average. In government lending, Hispanic borrowers alone are unable to capture rate declines occurring during the borrower's rate-lock period.     

Evidence of jointness in the terms of relationship lending

This paper examines the impact of the borrower–lender relationship on the explicit loan interest rate and collateral, as well as the correlation between loan interest rates and collateral. Using a simultaneous equation approach, we find that collateral has a statistically significant positive impact of 200 to 400 basis points on loan interest rates. We find this positive association to be stronger for personal (or outside) collateral than collateral provided by the firm's assets (or inside collateral). Finally, we find the economic impact of the borrower–lender relationship to be 21 basis points for one standard deviation increase in relationship length.     

Optimal Stopping and Losses on Subprime Mortgages

Lender losses on mortgage loans arise from a two-stage process. In the first stage, the borrower stops making payments if and when default is optimal. The second stage is a lengthy and costly period during which the lender employs legal remedies to obtain possession and execute a sale of the collateral. This research uses data on subprime mortgage losses to explore the role of borrower and collateral characteristics, and local legal requirements, as well as traditional option variables in the decisions of borrowers and lenders. Although subprime borrowers default earlier, which should reduce lender losses, these borrowers, nevertheless, impose greater realized losses on mortgage lenders.     

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).     

Exclusion,competition, and regulation in the retail loan market

Exclusion of borrowers from credit markets became a primary concern for regulators during the recovery from the recent recession. The paper analyzes loan-making institutions that set both interest rates and minimum credit requirements. We propose analytical measures of the degree of borrower exclusion from receiving loans. We analyze five market structures: Single lender, regulated interest rate, entry, interest rate discrimination, and highly-competitive lenders. Interest rate regulation improves total welfare relative to a single lender market. However, entry of a second lender reduces exclusion and generates higher total welfare. In the absence of fixed costs, perfect and Bertrand competition are optimal.     

Evaluating Real Estate Valuation Systems

A framework for comparing real estate valuation systems (including automated valuation models (AVMs) and current appraisal methods) is proposed. The density estimation and profit simulation (DEPS) method measures quality of a valuation system by simulating benefits to the mortgage lender who uses this method in mortgage underwriting to limit mortgage portfolio losses due to default. Related simple measures relevant to the selection of a valuation system are also discussed: skewness of the distribution of errors, correlation of valuation errors with current selling price errors, correlation of errors of the valuation system with errors of valuation systems used by competing mortgage lenders, and other measures.     

Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation

We use a contingent claims framework for valuing the the default and prepayment embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). This methodology provides a template for the borrower, lender, and insurer to compare mortgage terms, including the fairness of contract rates, arrangement fees, prepayment penalties, any MIG premiums required, and co-insurance exposure. With empirical inputs, this model may eventually be useful as a mark-to-value proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining valued added accounting, appropriate reserves, and indeed for setting premiums and business drivers. Fixed-rate endowment mortgages differ from fixed-rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We compare endownment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatilities.     

The Optimal Choice for Lenders Facing Defaults: Short Sale,Foreclose, or REO

When mortgage borrowers default and have no desire or ability to keep their property, then loss mitigation involves a sale of the property via one of the following options: (1) the lender allows pre-foreclosure “short sale” by the borrower, (2) the lender institutes the foreclosure process under a notice of default and the property is sold during the process by the borrower, and (3) the lender forecloses on the property, takes title, and sells the property in the market as real estate owned (REO). Sale of the property in the above three options is conducted by a motivated seller, either the owner or the lender, who desires to sell the property as quickly as possible. Thus, relative to a no-default sale, the house is most likely to be sold at a discounted price. It is generally expected that the discount would be lower in the case of a “short sale.” This option, however, may result in a longer marketing time, thus a higher total loss, than the other two options. We developed a model that allows simultaneous estimation of price and time-on-market effects of “short sales,” foreclosures, and REO options. We find that the short-sale option has the lowest-price discount, but significantly higher costs associated with marketing time. The pattern of price discount and marketing time reverses as we move to a sale while in the process of foreclosure and to a sale with an REO status.     

Double leverage cycle,interest rate,and financial crisis

We view mortgage as a risky derivative of its underlying house collateral and combine no-arbitrage valuation with equilibrium valuation approaches to develop a dynamic model of leverage cycle and interest rate. This model provides a unified explanation to pro-cyclical optimism, asset prices, and leverage, and counter-cyclical volatility and interest rate. In addition, the model shows that tightening funding margin in the mortgage securities market dampens optimism, asset prices, and leverage, whereas it raises volatility and interest rate in the housing market. A double leverage cycle leads to more volatile markets and a severe leverage cycle, thus resulting in worse financial crises.     

On the valuation of reverse mortgage insurance

This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Lévy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adjusted periodically according to the LIBOR rate, our finding reveals that the LTV ratio is insensitive to the parameters characterizing the CIR model.     

Mortgage Delivery to the Secondary Market when Interest Rates are Falling

A borrower whose loan is committed to the securitization process has the ability and incentive to switch lenders if market rates drop during the loan origination period, which creates significant exposure for primary lenders. A simple secondary market contract innovation we call a mortgage rate drop guarantee (MRDG) could shift this risk to the securitizers who represent portfolio investors. Our simulation results indicate this shifting would have improved the risk/return distribution faced by originators without damaging the risk/return position of securitizers during our 1977–2010 sample period. Assuming conservative loan lives and origination periods, and competitive lending markets, the risk reduction features of MRDGs could also have generated significant interest savings for borrowers.     

The economic role of foreclosures

We consider the economic consequences of changing the foreclosure rules. By incorporating renegotiation into the analysis, we show that although renegotiation decreases the number of foreclosures it can make the effects of foreclosure more significant. Even when foreclosure does not actually occur, a change in foreclosure rules changes the threat points of lender and borrower in any renegotiation, and thus changes the effective interest rate that the lender receives. In the long run, stated interest rates on loans will adjust to compensate for any change in the effective interest rate. We also examine the impact of a change in foreclosure laws on the borrower's welfare.     

Investment,agency conflicts,debt maturity,and loan guarantees by negotiation

We consider an irreversible investment, of which the sunk cost is financed by a finite-term debt after entering into an option-for-guarantee swap (OGS) with negotiation. The OGS is a three-party agreement among a lender (bank), an insurer, and a borrower (entrepreneur), where the bank lends at a given interest rate to the entrepreneur and if the borrower defaults on debt, the insurer must pay all the principal and remaining interests to the lender instead of the borrower. In return for the guarantee, the borrower must allocate a perpetual American call option to purchase a fraction (guarantee cost) of his equity at a given strike price. We find that the investment threshold decreases but the exercise threshold of the insurer’s option increases with the borrower’s bargaining power. Both the investment and exercise threshold increase with debt maturity, but there is a U-shaped relation between the guarantee cost and debt maturity. The borrower postpones investment once the funding gap or project risk increases. The swap may overcome the inefficiencies from asset substitution and debt overhang, strongly depending on the debt maturity and borrower’s bargaining power.     

Government intervention in the mortgage market: A study of anti-redlining regulations

This paper addresses the question of whether economic incentives exist for mortgage lenders to avoid or to minimize mortgage originations in neighborhoods inhabited primarily by low-income racial minorities. The Option Pricing Model is utilized to determine what mortgage borrower characteristics affect the market value of the mortgage contracts. It is found that existing laws do not enable mortgage lenders to vary either origination prices or mortgage terms so as to adjust for differences in the market values of mortgages. As a result, incentives are created for both the mortgage lender and the mortgage insurer to avoid originations and underwritings in areas with relatively high default probabilities. Various changes in mortgage lending regulations are suggested to eliminate these incentives, and the effects of alternative programs to subsidize mortgage borrowers with relatively high default probabilities are considered.