Mortgage contract design and systemic risk immunization

This paper provides theoretical results for the design of contracts used in the market for residential household mortgages and mortgage securities. Critical elements in the problem of immunizing systemic risk through efficient contract design are identified. Using an extension of classical immunization theory, this paper demonstrates that systemic risk of long amortization mortgage contracts is reduced when term to maturity of the contract at origination is significantly less than the amortization period. In addition, incorporating prepayment and limited recourse default options into the mortgage contract increases systemic risk when compared with full recourse mortgage contracts having yield maintenance prepayment penalties. The theoretical results are used to evaluate the systemic risk management problems that have plagued the US mortgage funding system.     

Adverse Selection in a Model of Real Estate Lending

We provide a rationale for the presence of points in mortgage loan contracts. Our analysis builds on two key features. First, insurance markets are unavailable for labor income. Second, the “due-on-sale” clause allows banks to offer loan contracts which partially insure against fluctuations in labor income. If explicit prepayment penalties are prohibited by law, points serve effectively as prepayment penalties. We also examine environments where such penalties are not prohibited and show that points will be used if interest rates cannot depend on the size of the loan.     

Commercial Mortgage-Backed Securities: Prepayment and Default

One of the major developments in real estate finance during the 1990s was the emergence of a viable market for commercial mortgage backed securities. The growth in this market has spurred greater interest in empirical and theoretical research on commercial mortgage default and prepayment. We employ a competing risks model to examine the default and prepayment behavior of commercial loans underlying CMBS deals. We find that changes in the yield curve have a direct impact on the probability of mortgage termination. Furthermore, we do not find any statistical relationship between LTV and prepayment or default.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

The probability of prepayment

Prepayment is a risk of holding a mortgage or derivative security. Incorrect pricing of prepayment risk leads to increased volatility and uncertainty in mortgage security markets. This article prices prepayment risk within an underlying callable bonds model. To price mortgages accurately, a probability of prepayment is required. A mortgage is a callable bond with a package of an option to prepay currently and a sequence of options to prepay up to the date of maturity. This sequence is summarized by a compound option. The probability of prepayment is determined by the prices of the current call and this compound option. These option prices depend on market interest rates and age, and on the contract terms of the originated mortgage.     

Residential Mortgage Lending and Borrower Risk: The Relationship Between Mortgage Spreads and Individual Characteristics

The mortgage banking environment in Hong Kong is quite different from that in the United States. For example, the secondary mortgage market and mortgage insurance only started after 1997. Using a large data set on mortgages, we examine empirically how mortgage rates in this market vary with various individual borrower, property, and loan characteristics. We find that mortgage rates in Hong Kong do vary with individual characteristics, which suggests credit sorting according to both prepayment risk and default risk, as a higher mortgage rate is found to be related to either higher collateral (a lower loan-to-value ratio) or slower prepayment. The empirical results suggest that lenders in Hong Kong can observe the risk type of individual borrowers to a certain extent and charge a corresponding mortgage spread. Overall, the evidence is consistent with the sorting-by-observed-risk paradigm as in Berger and Udell (1990).     

Anatomy of an ARM: The Interest-Rate Risk of Adjustable-Rate Mortgages

This article analyzes the dynamics of the commonly used indices for adjustable rate mortgages and systematically compares the effects of their time-series properties on the interest-rate sensitivity of adjustable-rate mortgages. Our ARM valuation methodology allows us simultaneously to capture the effects of index dynamics, discrete coupon adjustment, mortgage prepayment, and both lifetime and periodic caps and floors. We can, moreover, either calculate an optimal prepayment strategy for mortgage holders or use an empirical prepayment function. We find that the different dynamics of the major ARM indices lead to significant variation in the interest-rate sensitivities of loans based on different indices. We also find that changing assumptions about contract features, such as loan caps and coupon reset frequency, has a significant, and in some cases unexpected, impact on our results.     

Differential Impacts of Structural and Cyclical Unemployment on Mortgage Default and Prepayment

The Great Recession (the fourth quarter of 2007 through the second quarter of 2009) has been characterized by high rates of foreclosures and unemployment. Using a sample of community reinvestment loans, we examine the impact of structural unemployment and cyclical unemployment on mortgage terminations (default and prepayment). We find that mortgage default and prepayment are more sensitive to changes in the structural component of the local unemployment rate than in the cyclical component. In addition, depending on whether structural unemployment rates are high or low, borrowers and lenders react differently to the incentives to terminate a loan.     

An Analysis of Mortgage Contracting: Prepayment Penalties and the Due-on-Sale Clause

The due-on-sale clause contained in most conventional home mortgage contracts is equivalent to a prepayment penalty equal to the difference between the face value and market value of the loan. We analyze a bilateral game with asymmetric information and show that the bank demands the full penalty unless the market value of the loan is sufficiently low. In that case, the bank demands a prepayment penalty which is independent of the market value of the loan in order to induce additional prepayments. We also demonstrate, by a risk-sharing argument, that the due-on-sale clause is optimal in some settings, even though it eliminates some beneficial home sales.     

The timing of prepayment: A theoretical analysis

This article develops the analytical methods necessary to determine the prepayment patterns of a mortgage contract. The most obvious measure of how many years a mortgage is likely to last is the expected time to termination. It is this measure that we most fully explore. However, since the method employed is able to characterize the probability of prepayment in any given time period, the means is provided to determine any measure of the time to termination.     

Limits of Arbitrage: Theory and Evidence from the Mortgage-Backed Securities Market

“Limits of Arbitrage” theories hypothesize that the marginal investor in a particular asset market is a specialized arbitrageur rather than a diversified representative investor. We examine the mortgage‐backed securities (MBS) market in this light. We show that the risk of homeowner prepayment, which is a wash in the aggregate, is priced in the MBS market. The covariance of prepayment risk with aggregate wealth implies the wrong sign to match the observed prices of prepayment risk. The price of risk is better explained by a kernel based on MBS market‐wide specific risk, consistent with the specialized arbitrageur hypothesis.     

The role of prepayment penalties in mortgage loans

We study the effect of mortgage prepayment penalties on borrowers’ prepayments and delinquencies by exploiting a 2007 reform in Italy that reduced penalties on outstanding mortgages and banned penalties on newly-issued mortgages. Using a unique dataset of mortgages issued by a large Italian lender, we provide evidence that: 1) before the reform, mortgages issued to riskier borrowers included larger penalties; 2) higher prepayment penalties decreased borrowers’ prepayments; and 3) higher prepayment penalties did not affect borrowers’ delinquencies. Moreover, we find suggestive evidence that prepayment penalties affected mortgage pricing, as well as prepayments and delinquencies through borrowers’ mortgage selection at origination, most notably for riskier borrowers.     

Mortgage Prepayment and Default Behavior with Embedded Forward Contract Risks in China’s Housing Market

Most condominiums in China are sold forward on a pre-sale market, where purchasers and developers transact on an underlying property that is not yet completed. During the pre-sale period home buyers face a significant forward contract risk. However, home buyers can borrow mortgages from banks so that they can effectively share the forward contract risk with banks. This explains the phenomenon of irregularly high early-stage default and prepayment rates observed in residential mortgage lending in China, where there are few, if any, financial incentives for mortgage borrowers to exercise either put or call options. Mortgages collateralized by forward housing assets are riskier than are those with underlying assets traded on the spot market. However, currently Chinese mortgage banks charge the same rate to all mortgage borrowers. This inefficiency in risk sharing between mortgage borrowers’ groups in the forward and spot housing markets leads to mispricing in secondary mortgage sales and mortgage-backed security trading.     

Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.     

Duration and the price behavior of fixed-rate level payment mortgages: An analytical investigation

In this research we use a continuous payment formula for duration to examine the price behavior of a fixed-rate level payment mortgage. In the case where the mortgage is held to maturity, duration increases monotonically as term-to-maturity increases, regardless of changes in the market rate of interest. In the case where the mortgage is prepaid prior to maturity, there exists a unique market interest rate below which duration is a monotonically increasing function of time of prepayment, but above which duration has a global maximum at some time of prepayment prior to the term-to-maturity.     

PREPAYMENT RISK AND THE DURATION OF DEFAULT-FREE MORTGAGE-BACKED SECURITIES

The conventional duration measure for mortgage-backed pass-through securities assumes that the prepayment rate is invariant to changes in market interest rates. In this paper, the conventional duration is modified to take into account the interest-rate sensitivity of mortgage prepayments. Including interest rate sensitivity is shown to reduce substantially the duration of a mortgage-backed pass-through security when the current mortgage rate is less than the contract rate.     

An Early Assessment of Residential Mortgage Performance in China

The residential mortgage market becomes a financial engine for the booming residential housing development and sustained economic growth in China. Our study provides the first rigorous empirical analysis on the earlier performance of residential mortgage market in China based on a unique micro dataset of mortgage loan history collected from a major residential mortgage lender in China. We found that while the option theory fails to explain prepayment and default behavior in the residential mortgage market in China, other non-option theory related financial economic factors play major roles in determining the prepayment and default risks in China. We also found that borrower’s characteristics are significant in determining prepayment behavior, hence may be used as an effective tool for screening potential high risk borrowers in the loan origination process. Adopting a risk-based pricing in residential mortgage lending in China can improve the efficiency of the market, and enhance the credit availability to the most needed households, i.e., the younger households, blue-collar workers, lower income households, and help them become homeowners.     

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.     

Optimal Mortgage Contract Choice Decision in the Presence of Pay Option Adjustable Rate Mortgage and the Balloon Mortgage

The unprecedented run-up in global house prices of the 2000s was preceded by a revolution in U.S. mortgage markets in which borrowers faced a plethora of mortgages to choose from collectively known as nontraditional mortgages (NTMs), whose poor performance helped ignite the global financial crisis in 2007. This paper studies the choice of mortgage contracts in an expanded framework where the menu of contracts includes the pay option adjustable rate mortgage (PO-ARM), and the balloon mortgage (BM), alongside the traditional long horizon fixed rate mortgage (FRM) and the short horizon regular ARM. The inclusion of the PO-ARM is based on the fact it is the most controversial and perhaps the riskiest of the NTMs, whereas the BM has not been analyzed in the literature despite its different risk-sharing arrangement and long vintage. Our inclusive model relates the structural differences of these contracts to the horizon risk management problems and affordability constraints faced by the households that differ in terms of expected mobility. The numerical solutions of the model generates a number of interesting results suggesting that households select mortgage contracts to match their horizon, manage horizon risk and mitigate liquidity or affordability constraints they face. From a risk management and welfare perspectives, we find that the optimal contract for households with shorter horizons, specifically households who expect to move house once every 1 to 2 years, is the PO-ARM. Beyond 2 years the welfare advantage of the PO-ARM diminishes and BM becomes the more optimal contract up to 5-year horizon. Overall, the results suggest that households are neither as risk averse as the selection of the FRM would suggest, nor are they as risk-seeking as the selection of PO-ARM or regular ARM would suggest. The results also suggest that the exuberance demonstrated for NTMs by borrowers, especially PO-ARMs, may be both rational and irrational.     

An Improved Fixed-Rate Mortgage Valuation Methodology with Interacting Prepayment and Default Options

This paper considers in detail a realistic mortgage valuation model (including the potential for early prepayment and the risk of default), based on stochastic house-price and interest-rate models. As well as the development of a highly accurate numerical scheme to tackle the resulting partial differential equations, this paper also exploits singular perturbation theory (a mathematically rigorous procedure, based on the idea of the smallness of the volatilities), whereby mortgage valuation can be accurately approximated by very simple closed-form solutions. Determination of equilibrium contract rates, previously requiring many computational hours is reduced to just a few seconds, rendering this a highly useful portfolio management tool; these approximations compare favorably with the full numerical solutions. The method is of wide applicability in US or other mortgage markets and is demonstrated for UK fixed-rate mortgages, including insurance and coinsurance.