A Lattice Approach to Pricing Fixed-Rate Mortgages with Default and Prepayment Options

Existing models on the pricing of default and prepayment options in fixed-rate mortgages either use numerical methds or they do not consider refinancing or other transaction costs involved in default and prepayment. We provide in this paper an application of the Boyle [1] lattice model to price secured debt with two risky assets. This model is simple, efficient and capable of considering the major types of transaction costs involved in prepayment and default. Using our model, we estimate the option values under a range of assumptions about the underlying parameters. We also provide some comparisons of the lattice model estimates to other models in the literature.     

Rational Pricing of Adjustable Rate Mortgages

In this paper we develop a general method for valuing adjustable rate mortgages and by producing a set of simulation results, we show that our approach can be implemented. While the simulations are of interest in their own right, we view the approach itself as the major contribution of the paper.     

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.     

Pricing Life-of-Loan Rate Caps on Default-Free Adjustable-Rate Mortgages

A model is developed and utilized in this paper to value a life-of-loan interest-rate cap on an ARM that reprices monthly. The value of the cap is seen to depend importantly on both the slope of the term structure and the variance of the 1-month rate. However, the cap value is not sensitive to the source of the slope of the term structure — what precise combination of interest-rate expectations and risk aversion determined the slope. This insensitivity is fortunate because of the great difficulty of knowing at any point in time why the term structure is what it is.
Given the variation in the slope of the term structure and the variance of the 1-month rate that occurred over the 1979–84 period, the addition to the coupon rate on a 1-month ARM that lenders should have charged for a 5% life-of-loan cap has ranged from 5 to 40 basis points.     

Reverse Mortgages and Borrower Maintenance Risk

This paper develops a theoretical model of the problem of maintenance risk in reverse mortgages (RMs) and home equity conversion instruments generally. By maintenance risk, we refer to the incentive homeowners will have to reduce maintenance expenditures as their equity in the house falls during the term of the RM. The underlying reason for this tendency is the limited liability feature of RMs, given that a borrower's obligation to the lender at. maturity is limited to the value of the house.
The results of the model show that lenders will respond to this problem either by limiting the amount of RM loans to guarantee that maintenance risk is not a threat, or by charging an interest rate premium to cover the expected cost of default. Unfortunately, there do not exist data to test the importance of maintenance risk as a possible limitation on the extent of the RM market.     

Reverse Mortgages and Interest Rate Risk

We develop and apply a valuation model that quantifies the interest rate risk inherent in fixed-rate reverse mortgages. Consistent with intuition, our results show that the interest rate risk of a reverse mortgage is greater than that of either a typical coupon bond or a regular mortgage. Somewhat surprisingly, we find that this difference in interest rate risk is extremely large. In fact, the interest rate risk of a reverse mortgage often is several orders of magnitude greater than the interest rate risk of other fixed-income securities.     

Reverse Mortgages: Contracting and Crossover Risk

A pricing model is developed for a reverse mortgage contract where the borrower receives payments either as a lump sum or in an annuity while the loan balance accumulates as a claim against the house. No underwriting criteria on income are applied. One risk of default is that the borrower will remain in the house after the negatively amortizing loan balance exceeds the value of the house. An explicit pricing model of the reverse mortgage permits the evaluation of this default "crossover" option. Alternative methods involving life insurance contracts and securitization are compared as secondary market channels.     

Interest-Rate Volatility, Basis Risk and Heteroscedasticity in Hedging Mortgages

This paper investigates the validity of the OLS regression to estimate the hedge ratio for mortgages (GNMA) and provides alternative methodologies. In particular, this paper is concerned with the variance structure (conditional and unconditional heteroscedasticities) and the misspecification (nonlinearities) of the simple linear regression model for direct as well as cross-hedging. Using data on spot prices of GNMA and futures prices of GNMAs and T-bills for the period September 1979 to January 1985, we show that there exists significant heteroscedasticity particularly for cross-hedging, and nonlinearity between cash and futures prices for direct as well as cross-hedging. Alternative hedge ratio estimates are provided using the Box-Cox transformation model and an autoregressive conditional heteroscedastic (ARCH) Model.     

Commercial Mortgage Pricing with Unobservable Borrower Default Costs

This paper develops a pricing model for commercial real estate mortgage debt that recognizes the influence of default transaction costs on the borrower's default decision. These costs are heterogeneous across borrowers and largely un-observable to the lender/investor at the time of origination or loan purchase. A recognition of these unobservable costs can explain why borrower default decisions may differ from those predicted by "ruthless" mortgage-default pricing models. We address the determinants of default choice and timing by replacing sharp default boundaries found in the ruthless models with "fuzzy" boundaries that account for investor uncertainty with respect to evaluating borrower default decisions. To implement our model, we estimate probabilities of default as a junction of time and net equity in the property. Then, given that default occurs, loss severities are modeled based on expected property value recovery net of foreclosure costs and time until the asset is actually sold. Under reasonable parameter value choices, resulting Monte Carlo simulations produce numerical mortgage price estimates as well as component default frequency and severity levels that realistically reflect default premiums and loss levels observed in the marketplace.     

Differential Access to and Pricing of Home Mortgages: 2004 through 2009

This article documents trends and drivers of the residential mortgage market during the years 2004 through 2009, specifically focusing on the access to and pricing of mortgages originated by African‐American and Hispanic borrowers, and by borrowers living in low‐income and minority communities. Our analysis relies on a rich set of proprietary data that allow more expanded insights than can be obtained from the Home Mortgage Disclosure Act (HMDA) alone. We show that access to mortgage credit increased between 2004 and 2006 for the borrowers we focus on in our study and declined dramatically thereafter. Trends in access to credit were driven primarily by the changing credit mix of mortgage applicants and secondarily by the replacement of the Federal Housing Administration (FHA) for subprime as the dominant mode of nonprime originations and tighter underwriting standards. Throughout our entire period of study, these borrowers also consistently paid higher prices for their mortgages; however, the extent of this differential varied considerably over time and across groups. These pricing trends were driven primarily by changes in the FHA and subprime shares as well as by the market's increasingly aggressive pricing of credit risk.     

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.     

Interest Rate Risk, Residential Mortgages and Financial Futures Markets

Residential mortgage markets in both the United States and Canada have recently been dominated by instruments such as variable-rate and short-term rollover mortgages which require borrowers to assume a greater burden of interest rate risk. An outstanding question is whether this approach to risk allocation is Pareto optimal or whether there are other more effective methods of dealing with the risk created by interest rate volatility. This study examines the potential for shifting this risk from the mortgage market to the financial futures market. After considering the rationale for expecting that neither mortgage borrowers nor lenders wish to absorb the high levels of risk present in the existing financial environment, this study discusses the hedging of interest rate risk through financial futures markets. Empirical tests are then performed to evaluate the effectiveness of U.S. futures markets for hedging positions from the U.S. mortgage market. These results indicate that the interest rate risk inherent in residential mortgages can be substantially shifted through one or more positions in the existing futures contracts and long-term, fixed-rate mortgages may still be financially feasible under conditions of interest rate volatility.     

Regional Economic Stability and Mortgage Default Risk in the Netherlands

This paper investigates the relationship between regional economic diversification and stability, and residential mortgage default risk in the Netherlands. To describe and measure regional economic diversity and stability, methods from both the regional economics and the industrial economics literature are used. All measures are based on regional employment characteristics. Mortgage default rates were obtained from a database of the population of insured mortgage defaults in the Netherlands from 1983 through 1990. To test the relationship between the measures and mortgage default risk, cross sectional Seemingly Unrelated Regression was used. The paper concludes that the employed measures explain regional mortgage default rates to a significant extent, and that stability measures outperform diversity measures.     

On the Assessment of Default Risk in Commercial Mortgage Lending

This paper takes an initial step toward the development of an empirically-based model of default risk assessment in the commercial mortgage market. A review of existing empirical studies of residential mortgage and commercial loan default provides evidence for appropriate model specification and estimation. A simple default risk model for commercial mortgages is then developed based upon the generalized default risk models of Jackson and Kaserman [1980] and Vandell [1981]. The model is then examined for its ability to successfully handle a variety of situations and used to test the validity of traditional ratio analysis "rules-of-thumb" employed in commercial lending. Ratio tests are found generally to be inconsistent with an objective of constraining default risk below some maximum. Finally, a modified ratio analysis consistent with the model and with a constrained default risk strategy is introduced.     

Prepayment Risk in Adjustable Rate Mortgages Subject to Initial Year Discounts: Some New Evidence

This paper uses microlevel data to examine recent prepayment performance of adjustable rate mortgages (ARMs) employing the competing risk methodology developed by Deng, Quigley and Van Order (2000). We find support for the teaser rate and adjustment date effects implied by the theoretical model of Kau et al. (1993). In addition, we find that teased ARMs bear prepayment risk related to their discount, contrary to results reported by VanderHoff (1996) and Green and Shilling (1997). Finally, and contrary to the usual finding for fixed-rate mortgages, we find that loan age has a negative effect on prepayment risk for ARMs, consistent with the phenomenon that borrowers with high mobility and/or propensity to refinance exit the pool early.     

The Inevitability of Marketwide Underpricing of Mortgage Default Risk

Lenders are frequently accused of mispricing the put option embedded in nonrecourse lending. Prior research shows one lender's incentives to underprice. Here, we identify the conditions for a marketwide underpricing equilibrium. We demonstrate that, in a market with many players, given sufficient time, a race to the bottom and marketwide mispricing are inevitable. Underpricing occurs because bank managers and shareholders exploit mispriced deposit insurance. We show that the probability of the underpricing equilibrium increases with time since the previous market crash and that the more volatile the underlying asset market, the more likely it is subject to underpricing.     

Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages

This paper integrates two fundamentally important parameters into a theory of optimal mortgage design: the proportion of inflation risk borne by the lender / investor and the borrower and the amortization-graduation schedule for loan repayments. Equations are derived for a family of innovative mortgages, termed hybrid PLAMs, which offer advantages to borrowers and lenders over either the standard fixed rate mortgage (FRM) or the price level adjusted mortgage (PLAM). The superiority of the hybrid PLAMs lies in their ability to simultaneously and independently accommodate differing degrees of inflation-risk sharing and payment affordability. Inflation-risk sharing is represented by an indexation parameter set over a continuum of values such that the FRM has zero index variability and the PLAM has unit index variability. Similarly, payment tilt is represented by a tilt parameter such that the FRM has zero tilt and the PLAM has unit tilt. We demonstrate that these two parameters are independent and can each be continuously varied in a two-dimensional family of self-amortizing mortgages. A specific hybrid PLAM can be designed to partition inflation risk in any proportion between the borrower and the lender and to simultaneously prescribe any level of payment tilt between the extremes of the FRM and PLAM. The behavior of representative hybrid PLAMs is simulated and compared to FRMs and PLAMs for three different inflation scenarios, one of which uses actual market data from the period of 1960–1990.     

浅析利率调整对住房抵押贷款违约风险的影响

住房贷款利率的变化对房地产价格产生着巨大影响,房地产价格又是住房抵押贷款中重要因素,与住房抵押贷款风险密切相关。违约风险是住房低押贷款风险中最基本最主要的风险,也称信用风险。论文将从理论上分析利率政策调整对住宅抵押贷款违约风险的影响,并提出相应的防范措施。